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Table of Contents
Basic Number Problems
Number and Money Problems
Age and Digit Problems
Mixture Problems
Motion (D=RT) Problems
Test Review Problems
Test Review
Test Review
Systems of EquationsSystems of Equationschapter 6chapter 6
Word Problems:Word Problems:
MoneyMoney
Coins I tem Cost
Comparison
1 taco1 milk
Total $2.10
1 taco1 milk
Total $2.10
2 taco3 milk
Total $5.15
2 taco3 milk
Total $5.15
Find the cost of a tacoFind the cost of a tacoFind the cost of a tacoFind the cost of a taco
t cost of a tacom cost of a milk
Ex #1
Define variables:
1 taco1 milk
Total $2.10
1 taco1 milk
Total $2.10
2 taco3 milk
Total $5.15
2 taco3 milk
Total $5.15
t m 2.10
2t 3m 5.15
Ex #1
Write two equations:
Find the cost of a tacoFind the cost of a tacoFind the cost of a tacoFind the cost of a taco
t cost of a tacom cost of a milk
3
Solve the system
t m 2.10
2t 3m 5.15 3t 3m 6.30
2t 3m 5.15
t 1.15
Ex #1
t 1.15
taco $1.15
1 taco1 milk
Total $2.10
1 taco1 milk
Total $2.10
2 taco3 milk
Total $5.15
2 taco3 milk
Total $5.15
Ex #1
t 1.15
Find the cost of a tacoFind the cost of a tacoFind the cost of a tacoFind the cost of a taco
T cost of a tacoM cost of a milk
4r 5a4( 3.56)
Four Oranges and five apples cost $3.56. Three oranges and four apples cost $2.76. Find the cost of an orange.
Define variables:
Let r be the cost of an orange
Write two equations
E1
E2
Solve the system
An orange is $0.44
Let a be the cost of an Apple
4r 5a 3.56
3r 4a 2.76
3r 4a5( 2.76)
16r 20a 14.24 15r 20a 13.80
r 0.44
#2
A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar?
A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar?
Ex. #3Ex. #3Ex. #3Ex. #3
number of quarq tersnumber of dd imes
Define variables:
A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar?
A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar?
Ex. #3Ex. #3Ex. #3Ex. #3
q d 103
Define variables:
Write two equations 0.25q 0.10d 15.25
E1
E2
number of quarq tersnumber of dd imes
10
100
A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar?
A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar?
Ex. #3Ex. #3Ex. #3Ex. #3
q d 103
0.25q 0.10d 15.25
15q 495q 33
33 Quarters
Define variables:
25q 10d 1525
10q 10d 1030
number of quarq tersnumber of dd imes
Combined, Peyton and Eli have $106.75. Peyton has $43.75 more than Eli. How much money does Peyton have?
Combined, Peyton and Eli have $106.75. Peyton has $43.75 more than Eli. How much money does Peyton have?
Ex. #4Ex. #4Ex. #4Ex. #4
p e 106.75
Peyton's mp oney Eli'se money
p e 43.75
Peyton has $75.25Peyton has $75.25
2p 150.50p 75.25
Define variables:
Write two equations
E1
E2
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#1
At a football game, a popcorn and a soda purchased together costs $4.00. Three popcorns and five sodas would cost $16.50. What is the cost of a single soda?
Define variablesLet pp be the cost of a popcorn
Let s be the cost of a soda
Write two equationsE1
E2
p s 4.00 3p 5s 16.50
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#1
At a football game, a popcorn and a soda purchased together costs $4.00. Three popcorns and five sodas would cost $16.50. What is the cost of a single soda?
3p 3s 12.00 3p 5s 16.50
2s 4.50s 2.25Soda $2.25
Let pp be the cost of a popcorn
Let s be the cost of a soda
E1
E2
p s 4.00 3p 5s 16.50
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#2#2
Four apples and five bananas cost $3.75. Six apples and two bananas cost $2.82. What is the cost of a single banana?
Define variablesLet aa be the cost of 1 apple
Let b be the cost of 1 banana
Write two equationsE1
E2
4a 5b 3.75
6a 2b 2.82
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
4 6
#2#2
Four apples and five bananas cost $3.75. Six apples and two bananas cost $2.82. What is the cost of a single banana?
Let aa be the cost of 1 apple
Let b be the cost of 1 banana
4a 5b 3.75
6a 2b 2.82 24a 30b 22.50
24a 8b 11.28
22b 11.22b 0.51Banana $0.51
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
#3#3
d q 113
Define variables:Let dd be the number of dimes
Let q be the number of quarters
Write two equations
A vending machine takes only dimes and quarters. There are 113 coins in the machine totaling $17.60. How many quarters are in the machine?
0.10d 0.25q 17.60E1
E2
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
10
100
#3#3
d q 113
A vending machine takes only dimes and quarters. There are 113 coins in the machine totaling $17.60. How many quarters are in the machine?
0.10d 0.25q 17.60 10d 25q 1760
10d 10q 1130
15q 630q 4242 Quarters
Let dd be the number of dimes
Let q be the number of quarters
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#4#4
There are 40 coins in Jenny’s coin purse – all dimes and nickels. All together it adds to $2.65. How many nickels are in Jenny’s purse?
d n 40
0.10d 0.05n 2.65
Define variables:Let dd be the number of dimes
Let n be the number of nickels
Write two equations
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
10
100
#4#4
There are 40 coins in Jenny’s coin purse – all dimes and nickels. All together it adds to $2.65. How many nickels are in Jenny’s purse?
d n 40
0.10d 0.05n 2.65 10d 5n 265
10d 10n 400
5n 135n 2727 Nickels
Let dd be the number of dimes
Let n be the number of nickels
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
#5#5
L B 62.75
Combined, Bart and Lisa have $62.75. Lisa has $13.75 more than Bart. How much money does Bart have?
Let LL be Lisa’s money
Let B be Bart’s money
Define variables:
Write two equations
L B 13.75
2L 76.50L 38.25
Bart has $24.50
B 24.50
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
#6#6 Otis has three times as much money as Milo. Together they have $60.84. How much money does each one of them have?
Let tt be Otis’ money
Let m be Milo’s money
t m 60.84
t 3m 3t m
t 3m
?
3m m 60.84
4m 60.84
m 15.21t 45.63
Otis has $45.63
Milo has $15.21
Systems of EquationsSystems of Equationschapter 6chapter 6
Systems of EquationsSystems of Equationschapter 6chapter 6
Basic Word Problems:Basic Word Problems:Basic Word Problems:Basic Word Problems:
Example 1
The sum of two numbers is 49. One number is 13 less than the other. Find the numbers.
Define variables:
Let x be the larger number
Let y be the smaller number
Write two equations
E1
E2
Solve the system
x y 49 x y 13
x y 49 x y 13
2x 62x 31
y 1831 and 18
The difference between two numbers is 16. Threetimes the larger number is seven times the smaller. What are the numbers?Define variables:
Let x be the larger numberLet y be the smaller number
Write two equations
E1
E2
x y 16
3x 7y
x y 16
3 y 16 7y
3y 48 7y
48 4y
12 y
x 2812 and 28
Example 2
1
The sum of a number and twice The sum of a number and twice anotheranother number number is 13. The first number is 4 larger than the is 13. The first number is 4 larger than the second number. What are the two numbers?second number. What are the two numbers?
Define variables:
Let xx be the first number (larger)
Let yy be the second number
Write two equations
E1E2
Solve the system
Example 3
x 2y 13 x y 4
x 2y 13
x y 4
3y 9y 3x 77 and 3
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#3
The sum of two numbers is 82. One number is 12 more than the other. Find the larger number.
Define variables:
Let L be the larger numberLet S be the smaller number
Write two equations
E1
E2
L S 82
L S?
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#3
The sum of two numbers is 82. One number is 12 more than the other. Find the larger number.
Define variables:
Let L be the larger numberLet S be the smaller number
Write two equations
E1
E2
L S 82
L S 12
L S 12
L 12 S
L S L S 12
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#3
The sum of two numbers is 82. One number is 12 more than the other. Find the larger number.
Define variables:
Let L be the larger numberLet S be the smaller number
Write two equations
E1
E2
L S 82
L S 12
Solve the system
L S 12
L S 82
2L 94
L 4747
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#4
The difference between two numbers is 6. Ten times the smaller number is six times the larger. Find the numbers.
Define variables:
Let L be the larger numberLet S be the smaller number
Write two equations
E1
E2
L S 6
10S 6L
L S 6
10S 6 S 6
10S 6S 36
4S 36
S 9L 15
9 and 15
Solve the system
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#5#5
The sum of a number and twice another number is 37. The first number is 10 larger than the second number. What are the two numbers?
Define variables:
Let L be the larger numberLet S be the smaller number
Write two equations
E1
E2
L 2S 37
L S 10 L S 10
2S 0 S1 37
3S 10 37
3S 27
S 9L 19
9 and 19
Solve the system
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
The product of 4 times the sum of a number and 3 is another number. If the sum of the numbers is 67, what is the smallest of the two numbers?
Define variables:
Let x be one numberLet y be the “other” number
Write two equations
E1
E2
4 x 3 y
x y 67 4x 12 y
4x 12x 67
5x 12 67
5x 55x 11
y 5611
Solve the system
#6
Systems of EquationsSystems of Equationschapter 6chapter 6
Systems of EquationsSystems of Equationschapter 6chapter 6
More Word Problems:More Word Problems:More Word Problems:More Word Problems:
#1#1Farmer Bob had 25 animals in the barn – all of them either cows or chickens. He counted 66 legs in all. How many cows are in the barn?
w number of cowsk number of chickens
w k 25E1E2 4w 2k 66
2 w k 25 2w 2k 50
2w 16
w 8
8 cows 8 cows
The price of a ticket for the AVHS basketball game is $2.75 for a student, but only $2.25 if you have a discount card. One ticket taker sold 59 tickets for $141.75. How many students didn’t use a discount card?
The price of a ticket for the AVHS basketball game is $2.75 for a student, but only $2.25 if you have a discount card. One ticket taker sold 59 tickets for $141.75. How many students didn’t use a discount card?
Let xx be the number of students w/o discount cards
Let y be the number of students with discount cards
#2#2
x y 59
2.75x 2.25y 141.75 275x 225y 14,175
225x 225y 13,275
50x 900x 18
18 students w/ o discount card 18 students w/ o discount card
#3#3At Randy’s bike shop, they only work on bicycles and tricycles. When Randy disassembled all the bikes and trikes he ended up with 34 seats and 89 wheels. How many tricycles does he have in his shop?
At Randy’s bike shop, they only work on bicycles and tricycles. When Randy disassembled all the bikes and trikes he ended up with 34 seats and 89 wheels. How many tricycles does he have in his shop?
b number of bicycles
t number of tricycles
b t 34E1E2 2b 3t 89
2 b t 34 2b 2t 68
t 21
21 tricycles 21 tricycles
2b 3t 89
#4
Sydney took a math test that had 32 questions on it and scored 111 points. Each correct answer was awarded 5 points and for each wrong answer two points were deducted. How many questions did she miss on her test?
Sydney took a math test that had 32 questions on it and scored 111 points. Each correct answer was awarded 5 points and for each wrong answer two points were deducted. How many questions did she miss on her test?c correct answers
i incorrect answers
c i 32E1
E2 5c 2i 111
7i 49i 7She missed 7 questions.She missed 7 questions.
5c 5i 160
5c 2i 111
#5
Will set a school record by scoring 30 points in his basketball game. What was amazing is that he scored all his points without a single free-throw. Out of the 13 baskets that he made, how many were 3-point shots?
Will set a school record by scoring 30 points in his basketball game. What was amazing is that he scored all his points without a single free-throw. Out of the 13 baskets that he made, how many were 3-point shots?x 2-point shots
y 3-point shots
x y 13E1E2 2x 3y 30
y 4He made 4, 3-pointers.He made 4, 3-pointers.
2x 2y 26
2x 3y 30
100 25
#6#6
Jackie’s coin purse had only dimes and quarters in it. There were 5 more dimes than quarters, and the total amount of money was $7.85. How many dimes were in the purse?
Jackie’s coin purse had only dimes and quarters in it. There were 5 more dimes than quarters, and the total amount of money was $7.85. How many dimes were in the purse?
d number of dimes
q number of quarters
d q 5
0.10d 0.25q 7.85 10d 25q 785
25d 25q 125
35d 910d 2626 dimes26 dimes
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
#7#7
Let xx be the number of T/F questions
Let y be the number of “other” questions
x y 25
2x 3y 66
3x 3y 75
x 9x 99 T/ F questions. 9 T/ F questions.
A science test has 25 questions on it and is worth a total of 66 points. The true/false questions are worth 2 points each and the rest of the questions are worth 3 points each. How many true/false questions are on the test?
2x 3y 66
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
#8#8 At a movie theater, tickets cost $9.50 for adults and $6.50 for children. A group of 7 moviegoers pays a total of $54.50. How many adults are in the group?Let aa be the number of adults
Let c be the number of children
a c 7
9.50a 6.50c 54.50 95a 65c 545
65a 65c 455
30a 90a 33 adults 3 adults
T.G.I.F.T.G.I.F.T.G.I.F.
#1#1 At the baseball game field level seats cost $9.50 each, while seats in the second deck cost $6.25. If a ticket seller sold 52 tickets and collected $425.75, how many second deck seats did she sell?
Let ff be the number of field level tickets.
Let s be the number of 2nd deck tickets.
f s 52
9.50f 6.25s 425.75 950f 625s 42,575
950f 950s 49,400
325s 6,825s 2121 tickets21 tickets
T.G.I.F.T.G.I.F.T.G.I.F.
#4#4A History test has 40 questions on it and is worth a total of 174 points. The true/false questions are worth 3 points each and the rest of the questions are worth 5 points each. How many true/false questions are on the test?
t Number of T/ F questions.
r the "regular " questions.
t r 40E1E2 3t 5r 174
5 t r 40 5t 5r 200
2t 2613 T/ F questions 13 T/ F questions
3t 5r 174
t 13
T.G.I.F.T.G.I.F.T.G.I.F.
#6#6 A jar contains quarters and dimes. There are 15 more quarters than dimes. The total amount of money in the jar is $23. How many quarters are in the jar?
10
100
q d 15
0.25q 0.10d 23.00
35q 2450
q 7070 Quarters
q number of quartersd number of dimes
25q 10d 2300
10q 10d 150
T.G.I.F.T.G.I.F.T.G.I.F.
#7#7At the coffee shop, two bagels and three muffins cost $12.45. Three bagels and five muffins cost $20.00. What is the cost of a single bagel?
Let b be the cost of a bagel
E1
E2
Let m be the cost of a muffin
2b 3m 12.45
3b 5m 20.00
2b 3m 15( 2.45) 3b 5m3( 20.00)
10b 15m 62.25 9b 15m 60.00
b 2.25Bagel $2.25
T.G.I.F.T.G.I.F.T.G.I.F.
#10#10 The sum of two integers is 35 and the difference between the same two integers is 81. What is the smaller integer?
Let L be the larger number
Let S be the smaller number
E1
E2
L S 35 L S 81
2L 116
L 58
S 23
23 23
Haley was going to be paid to unpack a box of 125 delicate crystal ornaments. She would be paid 75 cents for each ornament unpacked, but would be charged $2.50 for any that she broke. After finishing the job she was paid $74.25. How many ornaments did she break?
Let xx be the number of ornaments unpacked successfully.
Let y be the number of ornaments broken
x y 125
0.75x 2.50y 74.25 75x 250y 7425
75x 75y 9375
325y 1950y 6
She broke 6 ornaments. She broke 6 ornaments.
#9- Bonus
Systems of EquationsSystems of Equationschapter 6chapter 6
Systems of EquationsSystems of Equationschapter 6chapter 6
Basic Word Problems:Basic Word Problems:• AgeAge• Number-DigitNumber-Digit
#1 The sum of the digits of a two-digit number is 10. When the digits are reversed, the new number is 54 more than the original number. What is the original number?
Let t be the tens digit of the original number
Let u be the units (ones) digit of the original number
E1:
E2:
10t u
t u 10
Original number New number
10u t
101 t tu u0 54 9u 9t 54
9u 9t 90
18u 144u 8t 2
28
#2 The sum of the digits of a two-digit number is 7. When the digits are reversed, the new number is 45 less than the original number. What is the original number?
Let t be the tens digit of the original number
Let u be the units (ones) digit of the original number
E1:
E2:
10t u
t u 7
Original number New number
10u t
101 t tu u0 45 9u 9t 45
9u 9t 63
18u 18u 1t 6
61
Andy is 21 years older than Bob. In two years, Andy Andy is 21 years older than Bob. In two years, Andy will be twice as old as Bob. What is Andy’s current will be twice as old as Bob. What is Andy’s current age? age?
Let a be Andy’s current age
Let b be Bob’s current age
Ex. 3
Age in 2 years
a 2b 2
E1:
E2:
a b 21
a 2 2b 4 a 2b 2 a 2 2 b 2
Andy is 21 years older than Bob. In two years, Andy Andy is 21 years older than Bob. In two years, Andy will be twice as old as Bob. What is Andy’s current will be twice as old as Bob. What is Andy’s current age? age?
Let a be Andy’s current age
Let b be Bob’s current age
Ex. 3
Age in 2 years
a 2b 2
E1:
E2:
a b 21
a 2b 2 2b 2 b 21b 19
a 40
a a
#4 Tom is 5 years older than Jerry. Last year Tom was twice as old as Jerry. How old is Tom today?
Let t be Tom’s current age
Let j be Jerry’s current age
Last year
t 1j 1
E1:
E2:
t j 5
t 1 2 j 1 t 1 2j 2 t 2j 1
#4 Tom is 5 years older than Jerry. Last year Tom was twice as old as Jerry. How old is Tom today?
Let t be Tom’s current age
Let j be Jerry’s current age
Last year
t 1j 1
E1:
E2:
t j 5
t 2j 1 j 5 2j 1
j 6t 11
t t
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#9#9
Let xx be the cost of an adult ticket
Let y be the cost of a youth ticket
E1
E2
6x 9y 402
6x 4y 292 2 3 2x 3y 134
3x 2y 146
5y 110
y 22$22 f or a youth ticket$22 f or a youth ticket
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
100 25
#10#10
Let xx be the number of Granny Smith apples
Let y be the number of Gala apples
x y 19
0.25x 0.30y 5.10
25x 25y 475
25x 30y 510
5y 35y 77 Gala and 12 Granny Smith
Let a be the measure of angle aLet b be the measure of angle b
E1
E2
a b 90
b 2a 12
m a 26
#2#2#2#2 Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.
Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.
E2 E1
2a 12a 90
3a 12 90
3a 78a 26
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems#7#7
Let xx be the cost of an adult ticket
Let y be the cost of a youth ticket
E1
E2
6x 9y 402
6x 4y 292 2 3 2x 3y 134
3x 2y 146
5y 110
y 22$22 f or a youth ticket$22 f or a youth ticket
Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems
100 25
#8#8
Let xx be the number of Granny Smith apples
Let y be the number of Gala apples
x y 19
0.25x 0.30y 5.10
25x 25y 475
25x 30y 510
5y 35y 77 Gala and 12 Granny Smith
#1#1#1#1
#2#2#2#2
Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year?
Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year?
Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.
Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.
#1#1#1#1 Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year?
Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year?
Let m be Marcus’s current age
Let k be Katie’s current age
Age last year
m 1k 1
E1:
E2:
m k 5 m 1 k 12
m 2k 1
m 1 2k 2 m 2k 1
#1#1#1#1 Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year?
Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year?
Let m be Marcus’s current age
Let k be Katie’s current age
Age last year
m 1k 1
E1:
E2:
m k 5
m 2k 1
m m
k 5 2k 1 5 k 16 kKatie will be 7 years-old next year.Katie will be 7 years-old next year.
Let a be the measure of angle aLet b be the measure of angle b
E1
E2
a b 90
b 2a 12
m a 26
#2#2#2#2 Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.
Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.
E2 E1
2a 12a 90
3a 12 90
3a 78a 26
10
#1#1A cashier is counting money at the end of the day. She has a stack that contains only $5 bills and $10 bills. There are 45 bills in the stack for a total of $290. How many $5 bills are in the stack?
F number of $5 bills
T number of $10 bills
F T 45E1E2 5F 10T 290
10F 10T 450
5T 160
32 $5-bills32 $5-bills
5F 10T 290
T 32
#2 The sum of the digits of a two-digit number is 13. When the digits are reversed the new number is 27 more than the original number. What was the original number?
Let t be the tens digit of the original number
Let u be the units (ones) digit of the original number
E1:
E2:
10t u
t u 13
Original number New number
10u t
101 u ut t0 27 9t 9u 27
9t 9u 117
18t 90
u 8t 558
Let d be Danielle’s current age
Let a be Alison’s current age
#3
Age 2 years ago
d 2a 2
E1:
E2:
d a 36 d 2 a 2
Danielle is 36 years older than her daughter Alison. Two years ago, Danielle was 5 times as old as Alison. Find Alison’s current age.
5
d 5a 8
d 2 5a 10
Let d be Danielle’s current age
Let a be Alison’s current age
#3
Age in 2 years
d 2a 2
E1:
E2:
d a 36
Danielle is 36 years older than her daughter Alison. Two years ago, Danielle was 5 times as old as Alison. Find Alison’s current age.
d 5a 8
d d
5a 8 a 36 4a 8 36
4a 44a 11
Alison is 11 years-oldAlison is 11 years-old
A jar contains 55 quarters and dimes. The total amount of money in the jar is $8.50. Find the number of dimes in the jar
#4#4
25
100
q d 55
0.25q 0.10d 8.50
15d 525
d 3535 dimes
25q 10d 850
25q 25d 1375
number of quarq tersnumber of dd imes
#5#5Becky is selling tickets to a school play. Adult tickets cost $12 and student tickets cost $6. Becky sells a total of 48 tickets and collects a total of $336. How many $6 tickets did she sell?
Becky is selling tickets to a school play. Adult tickets cost $12 and student tickets cost $6. Becky sells a total of 48 tickets and collects a total of $336. How many $6 tickets did she sell?
Let a be the number of adult tickets
Let s be the number of student tickets
E1:
E2:
a s 48
12a 6s 336 12a 6s 336
12a 12s 576
6s 240
s 4040 student tickets
#6The sum of the digits of a two-digit number is 14. The first digit is 4 less than twice the second digit. What is the number?
Let t be the tens digit of the numberLet u be the ones digit of the number
E1:
E2:
t u 14
t 2u 4
E2 E1
2u 4 u 14
3u 4 143u 18u 6
86
Five years ago, Beth was three times as old as Frank. Next year she will be twice as old as Frank. How old is Beth today?
#7#7
b is Beth’s current age
f is Frank’s current age
Age 5 years ago
b 5f 5
E1:
E2:
b 5 f 53
b 5 3f 15
Age next year
b 1f 1
b 3f 10
b 3f 10
Five years ago, Beth was three times as old as Frank. Next year she will be twice as old as Frank. How old is Beth today?
#7#7
b is Beth’s current age
f is Frank’s current age
Age 5 years ago
b 5f 5
E1:
E2:
Age next year
b 1f 1
b 3f 10 b 1 f 1
b 1 2f 2
b 2f 1 b 2f 1
2
Five years ago, Beth was three times as old as Frank. Next year she will be twice as old as Frank. How old is Beth today?
#7#7
b is Beth’s current age
f is Frank’s current age
Age 5 years ago
b 5f 5
E1:
E2:
Age next year
b 1f 1
b 3f 10
b 2f 1
b b
3f 10 2f 1 f 10 1
f 11Beth is 23 years-oldBeth is 23 years-old
Angle a and angle b are complementary angles. Angle b is 15 more than four times angle a. Find the measure of both angles.
#8#8
Let a be the measure of angle aLet b be the measure of angle b
E1
E2
a b 90
b 4a 15
m a 15
E2 E1
4a 15a 90
5a 15 90
5a 75a 15 m b 75
Systems of EquationsSystems of Equationschapter 6chapter 6
Systems of EquationsSystems of Equationschapter 6chapter 6
Basic Word Problems:Basic Word Problems:
• Mixture ProblemsMixture Problems
aa = amount of 12% solution
bb = amount of 20% solution
A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use?
A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use?
12% solution
18% solution
20% solution
#1#1#1#1
a b 300
0.12a 0.20b 54
Amount of Solution
Amount of alcohol
a b 300300
+ =
0.12a 0.20b
0.18(300) = 54
54
12%solution
20%solution
18%solution
A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use?
A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use?
#1#1#1#1
aa = amount of 12% solution
bb = amount of 20% solution
Amount of Solution
Amount of alcohol
a b 300300
+ =
0.12x 0.20y
0.18(300) = 54
54
12%solution
20%solution
18%solution
A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use?
A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use?
#1#1#1#1
aa = amount of 12% solution
bb = amount of 20% solution
a b 300
0.12a 0.20b 54
a 75
b 225
Amount of Solution
Amount of alcohol
a b 300300
+ =
0.12x 0.20y
0.18(300) = 54
54
12%solution
20%solution
18%solution
A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use?
A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use?
#1#1#1#1
aa = amount of 12% solution
bb = amount of 20% solution
a 75
b 22575 milliliters of 12% solution75 milliliters of 12% solution
225 milliliters of 20% solution225 milliliters of 20% solution
aa = amount of 30% solution
bb = amount of 50% solution
A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 Liters of a solution containing 42% insecticide. How much of each solution should be used?
A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 Liters of a solution containing 42% insecticide. How much of each solution should be used?
0.42(200) = 84
#2#2#2#2
Amount of Solution
Pureinsecticide
a b 200200
0.3a 0.5b 84
+ =30%solution
50%solution
42%solution
a b 200 0.3a 0.5b 84
aa = amount of 30% solution
bb = amount of 50% solution
A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 Liters of a solution containing 42% insecticide. How much of each solution should be used?
A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 Liters of a solution containing 42% insecticide. How much of each solution should be used?
#2#2#2#2
a b 200
0.3a 0.5b 84 3a 5b 840
3a 3b 600
10 3
2b 240b 120a 80
120 milliliters of 50% solution120 milliliters of 50% solution
80 milliliters of 30% solution80 milliliters of 30% solution
#3#3#3#3
c c = amount of Columbian beans (lbs.).
hh = amount of Hawaiian beans (lbs.)
Amount of Beans (lbs.)
Cost ofBeans ($)
c h 100100
1.50c 3.50h 270
+ =Columbian Hawaiian ChristmasBlend
c h 100
1.50c 3.50h 270
Starbucks wants to make 100 pounds of their special Christmas blend and sell it for $2.70 per pound. They will mix Columbian beans that sell for $1.50 per pound and Hawaiian beans that cost $3.50 per pound. How many pounds of the Hawaiian beans will they need to order?
Starbucks wants to make 100 pounds of their special Christmas blend and sell it for $2.70 per pound. They will mix Columbian beans that sell for $1.50 per pound and Hawaiian beans that cost $3.50 per pound. How many pounds of the Hawaiian beans will they need to order?
100
Starbucks wants to make 100 pounds of their special Christmas blend and sell it for $2.70 per pound. They will mix Columbian beans that sell for $1.50 per pound and Hawaiian beans that cost $3.50 per pound. How many pounds of the Hawaiian beans will they need to order?
Starbucks wants to make 100 pounds of their special Christmas blend and sell it for $2.70 per pound. They will mix Columbian beans that sell for $1.50 per pound and Hawaiian beans that cost $3.50 per pound. How many pounds of the Hawaiian beans will they need to order?
#3#3#3#3
c c = amount of Columbian beans (lbs.).
hh = amount of Hawaiian beans (lbs.)
c h 100
1.50c 3.50h 270 150c 350h 27000 150 150c 150h 15000
200h 12000h 60c 40
60 pounds of Hawaiian beans60 pounds of Hawaiian beans
Amount of Solution
Amount of Saline
a b 800800
+ =
0.3a 0.5b
0.45(800) = 360
360
30%solution
50%solution
45%solution
Jenny mixes a 30% saline solution with a 50% saline solution to make 800 milliliters of a 45% saline solution. How many milliliters of each solution does she use?
Jenny mixes a 30% saline solution with a 50% saline solution to make 800 milliliters of a 45% saline solution. How many milliliters of each solution does she use?
#1#1#1#1
aa = amount of 30% solution (ml)
bb = amount of 50% solution (ml)
a b 800
0.3a 0.5b 360
0.3a 0.5b 360
Jenny mixes a 30% saline solution with a 50% saline solution to make 800 milliliters of a 45% saline solution. How many milliliters of each solution does she use?
Jenny mixes a 30% saline solution with a 50% saline solution to make 800 milliliters of a 45% saline solution. How many milliliters of each solution does she use?
#1#1#1#1
aa = amount of 30% solution (ml)
bb = amount of 50% solution (ml)
a b 800
3a 5b 3600
3a 3b 2400
2b 1200b 600a 200
200 milliliters of 30% solution200 milliliters of 30% solution
600 milliliters of 50% solution600 milliliters of 50% solution
Amount of mix
Amount of aspirin
a b 1010
+ =
0.10a 0.25b
0.16(10) = 1.6
1.6
10% mix
25% mix
16% mix
A pharmacist wants to mix medicine that is 10% aspirin with a medicine that is 25% aspirin to make 10 grams of a medicine that is 16% aspirin. How many grams of each medicine should the pharmacist mix together?
A pharmacist wants to mix medicine that is 10% aspirin with a medicine that is 25% aspirin to make 10 grams of a medicine that is 16% aspirin. How many grams of each medicine should the pharmacist mix together?
#2#2#2#2
aa = amount of 10% mix (grams)
bb = amount of 25% mix (grams)
a b 10
0.10a 0.25b 1.6
A pharmacist wants to mix medicine that is 10% aspirin with a medicine that is 25% aspirin to make 10 grams of a medicine that is 16% aspirin. How many grams of each medicine should the pharmacist mix together?
A pharmacist wants to mix medicine that is 10% aspirin with a medicine that is 25% aspirin to make 10 grams of a medicine that is 16% aspirin. How many grams of each medicine should the pharmacist mix together?
#2#2#2#2
aa = amount of 10% mix (grams)
bb = amount of 25% mix (grams)
10a 25b 160
0.10a 0.25b 1.6
a b 10 10a 10b 100
15b 60b 4a 6
6 grams of 10% mix6 grams of 10% mix
4 grams of 25% mix4 grams of 25% mix
#3#3#3#3
p p = amount of peanuts (lbs.).
rr = amount of raisins (lbs.)
Weight of“stuff” (lbs.)
Cost of“stuff” ($)
p r 88
1.60p 2.40r 17.60
+ =Peanuts Raisins Mixture
p r 8
1.60p 2.40r 17.60
Peanuts cost $1.60 per pound and raisins cost $2.40 per pound. Brad wants to make 8 pounds of a mixture that costs $2.20 per pound. How many pounds of peanuts and raisins should he use?
Peanuts cost $1.60 per pound and raisins cost $2.40 per pound. Brad wants to make 8 pounds of a mixture that costs $2.20 per pound. How many pounds of peanuts and raisins should he use?
8(2.20) = 17.60
#3#3#3#3
p p = amount of peanuts (lbs.).
rr = amount of raisins (lbs.)
p r 8
1.60p 2.40r 17.60
Peanuts cost $1.60 per pound and raisins cost $2.40 per pound. Brad wants to make 8 pounds of a mixture that costs $2.20 per pound. How many pounds of peanuts and raisins should he use?
Peanuts cost $1.60 per pound and raisins cost $2.40 per pound. Brad wants to make 8 pounds of a mixture that costs $2.20 per pound. How many pounds of peanuts and raisins should he use?
16p 24r 176
16p 16r 128
8r 48r 6p 2
2 pounds of peanuts2 pounds of peanuts
6 pounds of raisins6 pounds of raisins
Systems of EquationsSystems of Equationschapter 6chapter 6
Systems of EquationsSystems of Equationschapter 6chapter 6
Basic Word Problems:Basic Word Problems:
• Motion ProblemsMotion Problems
Motion Problems Motion Problems Motion problems involve distance, time and rate.
The equation that links these concepts is called
The Distance Formula:
d = r td = distance
t = timer = rate
• milesmiles• kilometers kilometers • metersmeters• feetfeet• inchesinches
• hourshours• minutesminutes• secondsseconds• daysdays• yearsyears
• miles/hourmiles/hour• km/min. km/min. • m/sm/s• ft./sec.ft./sec.• inches/sec.inches/sec.
A jet airplane flies 2000 miles with the wind in four A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of hours. Find the speed of the jet and the speed of the wind. the wind.
A jet airplane flies 2000 miles with the wind in four A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of hours. Find the speed of the jet and the speed of the wind. the wind.
1111
Wind
d = 2000 miles t = 4 hours
A jet airplane flies 2000 miles with the wind in four A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of hours. Find the speed of the jet and the speed of the wind. the wind.
A jet airplane flies 2000 miles with the wind in four A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of hours. Find the speed of the jet and the speed of the wind. the wind.
1111
Wind
d = 2000 miles t = 4 hours
d = 2000 miles t = 5 hours
w = speed of windw = speed of wind
j = speed of the jetj = speed of the jet
Withthe wind
w = speed of windw = speed of wind
2000
Rate
1111
j = speed of the jetj = speed of the jet
A jet airplane flies 2000 miles with the wind in four A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of hours. Find the speed of the jet and the speed of the wind. the wind.
A jet airplane flies 2000 miles with the wind in four A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of hours. Find the speed of the jet and the speed of the wind. the wind.
Time Distance
Againstthe wind
4j w
j w 5 2000
j w 4 2000
j w 5 2000
w = speed of windw = speed of wind
1111
j = speed of the jetj = speed of the jet
A jet airplane flies 2000 miles with the wind in four A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of hours. Find the speed of the jet and the speed of the wind. the wind.
A jet airplane flies 2000 miles with the wind in four A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of hours. Find the speed of the jet and the speed of the wind. the wind.
j w 4 2000
j w 5 2000
4j 4w 2000
5j 5w 2000 20j 20w 8000
20j 20w 10,000
40j 18,000j 450w 50
Speed of the jet = 450 mphSpeed of the jet = 450 mph
Speed of the wind = 50 mphSpeed of the wind = 50 mph
Withthe current
c = speed of the current c = speed of the current (mph)(mph)
8
Rate
2222
b = speed that Ben can paddle in still water b = speed that Ben can paddle in still water (mph).(mph).
Ben paddles his kayak 8 miles upstream in 4 hours. Ben paddles his kayak 8 miles upstream in 4 hours. He turns around and paddles back downstream to his He turns around and paddles back downstream to his starting point in just 2 hours. What is the speed of starting point in just 2 hours. What is the speed of the current?the current?
Ben paddles his kayak 8 miles upstream in 4 hours. Ben paddles his kayak 8 miles upstream in 4 hours. He turns around and paddles back downstream to his He turns around and paddles back downstream to his starting point in just 2 hours. What is the speed of starting point in just 2 hours. What is the speed of the current?the current?
Time Distance
Againstthe current
2b c
b c 4 8
b c 2 8
b c 4 8
c = speed of the current (mph)c = speed of the current (mph)
2222
b = speed that Ben can paddle in still water (mph).b = speed that Ben can paddle in still water (mph).
Ben paddles his kayak 8 miles upstream in 4 hours. Ben paddles his kayak 8 miles upstream in 4 hours. He turns around and paddles back downstream to He turns around and paddles back downstream to his starting point in just 2 hours. What is the speed his starting point in just 2 hours. What is the speed of the current?of the current?
Ben paddles his kayak 8 miles upstream in 4 hours. Ben paddles his kayak 8 miles upstream in 4 hours. He turns around and paddles back downstream to He turns around and paddles back downstream to his starting point in just 2 hours. What is the speed his starting point in just 2 hours. What is the speed of the current?of the current?
b c 2 8
b c 4 8
2b 2c 8
4b 4c 8 4b 4c 16 4b 4c 8
8b 24b 3
c =1
Speed of current = 1 mphSpeed of current = 1 mph
Speed that ben can paddle = 3 mphSpeed that ben can paddle = 3 mph
Systems of EquationsSystems of Equationschapter 6chapter 6
Systems of EquationsSystems of Equationschapter 6chapter 6
Test ReviewTest Review
Withthe wind
w = speed of windw = speed of wind
300
Rate
1111
c = speed of the helicopterc = speed of the helicopter
With a tailwind, a helicopter flies 300 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter’s speed in still air? What is the speed of the wind?
With a tailwind, a helicopter flies 300 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter’s speed in still air? What is the speed of the wind?
Time Distance
Againstthe wind
1.5c w
c w 3 300
c w 1.5 300
c w 3 300
1111
1.5c 1.5w 300
3c 3w 300 3c 3w 300
3c 3w 600
6c 900c 150w 50
Speed of the heli. = 150 mphSpeed of the heli. = 150 mph
Speed of the wind = 50 mphSpeed of the wind = 50 mph
w = speed of windw = speed of wind
c = speed of the helicopterc = speed of the helicopter
With a tailwind, a helicopter flies 300 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter’s speed in still air? What is the speed of the wind?
With a tailwind, a helicopter flies 300 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter’s speed in still air? What is the speed of the wind?
Withthe current
c = speed of currentc = speed of current
24
Rate
2222
b = speed of the bargeb = speed of the barge
A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.
A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.
Time Distance
Againstthe current
2b c
b c 3 24
b c 2 24
b c 3 24
2b 2c 24
3b 3c 24 b c 8
b c 12
2b 20b 10c 2
Speed of the barge = 10 mphSpeed of the barge = 10 mph
Speed of the current = 2 mphSpeed of the current = 2 mph
c = speed of currentc = speed of current
b = speed of the bargeb = speed of the barge
2222 A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.
A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.
Amount of Solution
Amount of Acid
a b 500500
+ =
0.1a 0.2b
0.16(500) = 80
80
10%solution
20%solution
16%solution
A chemist mixes a 10% acid solution with a 20% acid solution to make 500 milliliters of a 16% acid solution. How much of the 20% solution did he use in his mixture?
A chemist mixes a 10% acid solution with a 20% acid solution to make 500 milliliters of a 16% acid solution. How much of the 20% solution did he use in his mixture?
#3#3#3#3
aa = amount of 10% acid solution (ml)
bb = amount of 20% acid solution (ml)
a b 500
0.1a 0.2b 80
A chemist mixes a 10% acid solution with a 20% acid solution to make 500 milliliters of a 16% acid solution. How much of the 20% solution did he use in his mixture?
A chemist mixes a 10% acid solution with a 20% acid solution to make 500 milliliters of a 16% acid solution. How much of the 20% solution did he use in his mixture?
#3#3#3#3
a 2b 800 −a−b −500
b =300
a 200200 ml of 10% acid solution200 ml of 10% acid solution
300 ml of 20% acid solution300 ml of 20% acid solution
aa = amount of 10% acid solution (ml)
bb = amount of 20% acid solution (ml)
a b 500
0.1a 0.2b 80
#4#4#4#4
a a = amount of apricots (lbs.).
cc = amount of cherries (lbs.)
Weight of“stuff” (lbs.)
Cost of“stuff” ($)
a c 2020
1.50a 3.50c 54
+ =apricots cherries Mixture
a c 20
1.50a 3.50c 54
At the Snack Shack, dried cherries cost $3.50 per pound. Dried apricots cost $1.50 per pound. The store’s owner wants to make 20 pounds of a mixture that costs $2.70 per pound. How many pounds of cherries will be needed to make the mixture?
At the Snack Shack, dried cherries cost $3.50 per pound. Dried apricots cost $1.50 per pound. The store’s owner wants to make 20 pounds of a mixture that costs $2.70 per pound. How many pounds of cherries will be needed to make the mixture?
20(2.70) = 54
#4#4#4#4
15a 35c 540
15a 15c 300
20c 240c 1212 pounds of cherries12 pounds of cherries
a c 20
1.50a 3.50c 54
At the Snack Shack, dried cherries cost $3.50 per pound. Dried apricots cost $1.50 per pound. The store’s owner wants to make 20 pounds of a mixture that costs $2.70 per pound. How many pounds of cherries will be needed to make the mixture?
At the Snack Shack, dried cherries cost $3.50 per pound. Dried apricots cost $1.50 per pound. The store’s owner wants to make 20 pounds of a mixture that costs $2.70 per pound. How many pounds of cherries will be needed to make the mixture?
a a = amount of apricots (lbs.).
cc = amount of cherries (lbs.)
Are You Ready For The Test?
Which system can solve the word problem given?
At the hardware store, 15 screws and 7 bolts weigh 303 grams. 12 bolts and 5 screws weigh 188 grams. What will 9 bolts weigh? b = weight of a bolt
s = weight of a screw
7b 15s 303
12b 5s 188
5b 12s 188
15b 7s 303
7b 15s 188
9b 5s 303
15b 7s 303
12b 5s 188
#1#1
Andy is 21 years older than Bob. In two years, Andy will be twice as old as Bob. What is Andy’s current age? Let a be Andy’s current age
Let b be Bob’s current age
a b 21
a 2 2b 4
a b 21
a 2 2b 4
a b 21
2a 4 b 2
a b 21
a 2 2b 2
#2#2