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ExerciseExerciseWhat is the value of seven nickels?What is the value of seven nickels?
$0.35$0.35
What is the value of fourteen quarters?What is the value of fourteen quarters?
$3.50$3.50
ExerciseExercise
Write two expressions for the value of d dimes, one in dollars and one in cents.
Write two expressions for the value of d dimes, one in dollars and one in cents.
0.1d and 10d0.1d and 10d
ExerciseExercise
Joe has 23 coins in his pocket. He has 7 nickels, and the rest of the coins are an equal number of dimes and quarters. How much money does he have?
Joe has 23 coins in his pocket. He has 7 nickels, and the rest of the coins are an equal number of dimes and quarters. How much money does he have?
$3.15$3.15
ExerciseExercise
Shannon has twice as many quarters as dimes; and the total number of her dimes, quarters, and pennies is 12. Write expressions for the numbers of quarters and pennies in terms of d, the number of dimes.
Shannon has twice as many quarters as dimes; and the total number of her dimes, quarters, and pennies is 12. Write expressions for the numbers of quarters and pennies in terms of d, the number of dimes.quarters: 2d; pennies: 12 – 3dquarters: 2d; pennies: 12 – 3d
ExerciseExercise
Money ProblemsMoney ProblemsIn the first type of problem, the total number of coins is known. The total value of the money is not.
In the first type of problem, the total number of coins is known. The total value of the money is not.
Ivan has been saving money and has 351 coins. He has three more quarters than twice the number of dimes. How many of each coin does he have? How much money does he have?
Ivan has been saving money and has 351 coins. He has three more quarters than twice the number of dimes. How many of each coin does he have? How much money does he have?
Example 1Example 1
Since the number of quarters is expressed in terms of the number of dimes, let d represent the number of dimes. Then express the number of quarters in terms of d.
Since the number of quarters is expressed in terms of the number of dimes, let d represent the number of dimes. Then express the number of quarters in terms of d.
CoinCoinDimesDimes
QuartersQuarters
Number of CoinsNumber of Coinsdd
2d + 32d + 3
d + (2d + 3) = 351d + (2d + 3) = 351(d + 2d) + 3 = 351(d + 2d) + 3 = 351
3d + 3 = 3513d + 3 = 351
3d + 3 – 3 = 351 – 33d + 3 – 3 = 351 – 3
3d = 3483d = 34833 33d = 116 dimesd = 116 dimes
351 – 116351 – 116 = 235 quarters= 235 quarters
116(0.10) + 235(0.25)116(0.10) + 235(0.25)= $70.35= $70.35
116 dimes116 dimes
Money ProblemsMoney ProblemsIn the second type of money problem, the total value of the money is known, but the number of coins of each denomination is not.
In the second type of money problem, the total value of the money is known, but the number of coins of each denomination is not.
Steve saves money by putting his dimes, nickels, and pennies in a jar. He has three times as many dimes as pennies and 18 more nickels than dimes. If he has a total of $14.24, find the number of dimes, nickels, and pennies he has.
Steve saves money by putting his dimes, nickels, and pennies in a jar. He has three times as many dimes as pennies and 18 more nickels than dimes. If he has a total of $14.24, find the number of dimes, nickels, and pennies he has.
Example 2Example 2
Notice that the number of dimes is described in terms of the number of pennies, and the number of nickels is described in terms of the number of dimes. It would be best to know the number of pennies first. Let p = the number of pennies.
Notice that the number of dimes is described in terms of the number of pennies, and the number of nickels is described in terms of the number of dimes. It would be best to know the number of pennies first. Let p = the number of pennies.
CoinCoin
NickelsNickels
DimesDimes
# of Coins# of
Coins
3p + 183p + 18
3p3p
PenniesPennies pp
55
1010
11
5(3p + 18)5(3p + 18)
10(3p)10(3p)
pp
Value of
Coins
Value of
Coins
Total ValueTotal Value
Each dollar is 100 cents, so he has 14.24(100) = 1,424 cents. This number will be used in the equation since the values of the coins in the table are given in cents.
Each dollar is 100 cents, so he has 14.24(100) = 1,424 cents. This number will be used in the equation since the values of the coins in the table are given in cents.p + 5(3p + 18) + 10(3p) = 1,424p + 5(3p + 18) + 10(3p) = 1,424
p + 15p + 90 + 30p = 1,424p + 15p + 90 + 30p = 1,42446p + 90 = 1,42446p + 90 = 1,424
46p + 90 – 90 = 1,424 – 9046p + 90 – 90 = 1,424 – 9046p = 1,33446p = 1,334
4646 4646p = 29 penniesp = 29 pennies
3p = 3(29)3p = 3(29) = 87 dimes= 87 dimes
3p + 18 = 3(29) + 183p + 18 = 3(29) + 18
= 105 nickels= 105 nickels
Shyla has twice as many dimes as nickels, and she has three more quarters than nickels. If her coins total $4.75, how many of each coin does she have?
Shyla has twice as many dimes as nickels, and she has three more quarters than nickels. If her coins total $4.75, how many of each coin does she have?
Example 3Example 3
CoinCoin
DimesDimes
QuartersQuarters
# of Coins# of
Coins
2n2n
n + 3n + 3
NickelsNickels nn
1010
2525
55
10(2n)10(2n)
25(n + 3)25(n + 3)
5n5n
Value of
Coins
Value of
Coins
Total ValueTotal Value
5n + 10(2n) + 25(n + 3) = 4755n + 10(2n) + 25(n + 3) = 4755n + 20n + 25n + 75 = 4755n + 20n + 25n + 75 = 475
50n + 75 = 47550n + 75 = 47550n + 75 – 75 = 475 – 7550n + 75 – 75 = 475 – 75
50n = 40050n = 4005050 5050
n = 8 nickelsn = 8 nickels2n = 2(8)2n = 2(8) = 16 dimes= 16 dimesn + 3 = 8 + 3n + 3 = 8 + 3 = 11 quarters= 11 quarters
George has 29 coins, made up of quarters and nickels. If their total value is $4.85, how many of each coin does he have?
George has 29 coins, made up of quarters and nickels. If their total value is $4.85, how many of each coin does he have?
Example 4Example 4
CoinCoin
QuartersQuarters
# of Coins# of
Coins
NickelsNickels 29 – q29 – q
2525
55
25q25q
5(29 – q)5(29 – q)
Value of
Coins
Value of
Coins
Total ValueTotal Value
5(29 – q) + 25q = 4855(29 – q) + 25q = 485
q = 17 quartersq = 17 quarters29 – q = 29 – 1729 – q = 29 – 17 = 12 nickels= 12 nickels
145 – 5q + 25q = 485145 – 5q + 25q = 485145 + 20q = 485145 + 20q = 485
145 – 145 + 20q = 485 – 145145 – 145 + 20q = 485 – 14520q = 34020q = 3402020 2020
Joe has 50 nickels and dimes. The number of dimes is five more than twice the number of nickels. How many of each does he have?
Joe has 50 nickels and dimes. The number of dimes is five more than twice the number of nickels. How many of each does he have?
ExampleExample
15 nickels and 35 dimes15 nickels and 35 dimes
ExampleExample
Lucy has 70 nickels, dimes, and quarters. The number of dimes is five more than twice the number of nickels, and the number of quarters is five more than three times the number of nickels.
Lucy has 70 nickels, dimes, and quarters. The number of dimes is five more than twice the number of nickels, and the number of quarters is five more than three times the number of nickels.
ExampleExample
How many of each does she have?How many of each does she have?
10 nickels, 25 dimes, and 35 quarters
10 nickels, 25 dimes, and 35 quarters
ExampleExample
Vern has 180 nickels, dimes, and quarters. He has ten more dimes than nickels and as many quarters as he has nickels and dimes combined. How many of each does he have?
Vern has 180 nickels, dimes, and quarters. He has ten more dimes than nickels and as many quarters as he has nickels and dimes combined. How many of each does he have?
ExampleExample
40 nickels, 50 dimes, and 90 quarters
40 nickels, 50 dimes, and 90 quarters
ExampleExample
Ricardo has 90 pennies, nickels, and dimes. He has twice as many nickels as pennies and 50% more dimes than nickels. How many of each does he have?
Ricardo has 90 pennies, nickels, and dimes. He has twice as many nickels as pennies and 50% more dimes than nickels. How many of each does he have?
ExampleExample
15 pennies, 30 nickels, and 45 dimes
15 pennies, 30 nickels, and 45 dimes
ExampleExample
John has 120 coins in pennies, nickels, dimes, and quarters. He has twice as many nickels as pennies and twice as many quarters as dimes.
John has 120 coins in pennies, nickels, dimes, and quarters. He has twice as many nickels as pennies and twice as many quarters as dimes.
ExampleExample
16 pennies, 32 nickels, 24 dimes, and 48 quarters
16 pennies, 32 nickels, 24 dimes, and 48 quarters
ExampleExampleIf the number of dimes is half the total number of nickels and pennies, how many of each does he have?
If the number of dimes is half the total number of nickels and pennies, how many of each does he have?
Gary has $421 in ones and fives. The number of ones is one more than twice the number of fives. How many of each does he have?
Gary has $421 in ones and fives. The number of ones is one more than twice the number of fives. How many of each does he have?
ExampleExample
60 fives and 121 ones60 fives and 121 ones
ExampleExample
Wren notices at the end of the day that there is $4.10 in change in the cash register and, interesting enough, the number of pennies, nickels, dimes, and quarters are exactly the same. How many of each coin are there?
Wren notices at the end of the day that there is $4.10 in change in the cash register and, interesting enough, the number of pennies, nickels, dimes, and quarters are exactly the same. How many of each coin are there?
ExampleExample
10 of each10 of each
ExampleExample
Zhi withdraws $60 from the bank each Friday so he will have enough change for his store’s cash registers over the weekend. He always gets twice as many nickels and dimes as quarters...
Zhi withdraws $60 from the bank each Friday so he will have enough change for his store’s cash registers over the weekend. He always gets twice as many nickels and dimes as quarters...
ExampleExample
...and five times as many pennies as quarters.
How many of each coin does he get?
...and five times as many pennies as quarters.
How many of each coin does he get?
100 quarters, 200 dimes, 200 nickels, and 500 pennies
100 quarters, 200 dimes, 200 nickels, and 500 pennies
ExampleExample
Hans withdraws $255 from his savings. He asks the teller to give him twice as many fives as ones and twice as many tens as fives. How many of each bill will he receive?
Hans withdraws $255 from his savings. He asks the teller to give him twice as many fives as ones and twice as many tens as fives. How many of each bill will he receive?
ExampleExample
5 ones, 10 fives, and 20 tens5 ones, 10 fives, and 20 tens
ExampleExample
Heidi wants to withdraw $3,500 from her savings. She asks for five hundreds, and she wants the rest to be divided so she has the same number of ones, fives, tens, and twenties. Can this be done?
Heidi wants to withdraw $3,500 from her savings. She asks for five hundreds, and she wants the rest to be divided so she has the same number of ones, fives, tens, and twenties. Can this be done?
ExampleExample
n = 83.33; No, this cannot be done since n is not an integer.n = 83.33; No, this cannot be
done since n is not an integer.
ExampleExample
Mr. Cohen’s net worth is twice as much as Mr. Hall’s and three times as much as Mr. Chang’s. They claim that their combined net worth is a million dollars.
Mr. Cohen’s net worth is twice as much as Mr. Hall’s and three times as much as Mr. Chang’s. They claim that their combined net worth is a million dollars.
ExerciseExercise
Find the net worth of each one to the nearest dollar.Find the net worth of each one to the nearest dollar.
Mr. Chang: $181,818; Mr. Hall: $272,727;
Mr. Cohen: $545,455
Mr. Chang: $181,818; Mr. Hall: $272,727;
Mr. Cohen: $545,455
ExerciseExercise
A roll of 36 bills contains two more twenties than fifties, eight fewer tens than twenties, and twice as many fives as fifties. How many of each bill are in the roll? How much money is in the roll of bills?
A roll of 36 bills contains two more twenties than fifties, eight fewer tens than twenties, and twice as many fives as fifties. How many of each bill are in the roll? How much money is in the roll of bills?
ExerciseExercise
8 fifties, 10 twenties, 2 tens, and 16 fives; $700
8 fifties, 10 twenties, 2 tens, and 16 fives; $700
ExerciseExercise
