Algebra 22.2

Pinkston

SAT QuestionIf 16 2k , what is the value of k?

A. 1B. 2C. 3D. 4E. 8

216 4 2

Review of words to translate English into algebra:

Addition: sum, total, increased by, more than, plus, longer than

Subtraction: difference, decreased by, less than, subtracted from, minus; fewer than, less (Those in italics and blue switch the

order from English to algebra).Multiplication: product, times, twice, of,

double, tripleDivision: quotient, over, divided by, ratioEquality: is, the result is, equals, is the

same as

Don’t confuse less than (subtraction) with is less than (<)

Translate:1. The ratio of a number and 4.2. Two-thirds of a number.3. The difference between 5 and a

number.4. The sum of a number and 3.

4

x

2

3x

5 x3x

5. Ten fewer than a number.6. The product of a number and 3.7. A number decreased by 15.8. Three times the sum of a number

and 6.9. The sum of the quantity three times

a number and 6.10. The average of x and y.

11. Thirty percent of a number.

10x 3x15x

3( 6)x

3 6x

2

x y

0.3x

Solving Word Problems

1. _________________________________

2. _________________________________

3. _________________________________

4. _________________________________

Heading

Equation

Solve

Solution

Example 1: A 28-ft rope is cut into two pieces. One piece is 3 ft longer than the other. How long are the pieces?Heading:

Equation:

(Solve)

Solution:

3

first piece x

other piece x

3 28x x 2 3 28x

2 25x 12.5x

12.5 15.5ft and ft

Example 2: A 23-ft cable is cut into two pieces, one three times as long as the other. How long are the pieces?Heading:

Equation:

(Solve)

Solution:

3

first piece x

other piece x

3 23x x 4 23x

5.75x 3 17.25x

5.75 17.25ft and ft

Example 3: Five plus twice a number is seven times the number. What is the number?Heading:

Equation:

(Solve)

Solution:

the number x

5 2 7x x 5 5x1 x

1

Example 4: If seven times a certain number is subtracted from 6, the result is five times the number. What is the number? Heading:

Equation:

(Solve)

Solution:

the number x

6 7 5x x

1

2x

6 12x

1

2

Example 5: Chris bought a baseball card in 1975. By 1985, the value of the card had tripled. Since 1985, the value has increased by another $30. The card is now worth 5 times its original value. How much was the card worth when Chris bought it?

Heading:

Equation:

(Solve)

Solution:

1985 3

3 30

original value x

valuein x

value now x

3 30 5x x

$15

30 2x15 x

Example 6: A clothing store drops the price of a suit 25% to a sale price of $93. What was the original price of the suit? Heading:

Equation:

(Solve)

Solution:

.25

original price x

sale price x x

.25 93x x

$124

.75 93x 124x

Example 7: An investment is made at 12% simple interest. It grows to $812 at the end of one year. How much was invested originally? Formula for final amount of money (called “future value”): A = P + Prt P is Principal; r is rate (%); t is time in years.

Heading:

Equation:

(Solve)

Solution:

Principal P

812 (.12)(1)P P 812 .12P P 812 1.12P725 P$725

Example 8: The sum of two consecutive even integers is 50. What are the integers?

Heading:

Equation:

(Solve)

Solution:

2

x

x

2 50x x

24 26and

2 2 50x

24x 2 48x

Example 9: Find four consecutive integers such that the sum of the second and fourth is 132.

Heading:

Equation:

(Solve)

Solution:

1

2

3

x

x

x

x

1 3 132x x

64, 65, 66, 67

2 4 132x

64x 2 128x

Example 10: The second angle of a triangle is four times the first and the third is 5° more than twice the first. Find the measures of the angles.The three angles of a triangle add up to 180°.

Heading:

Equation:

(Solve)

Solution:

1

2 4

3 5 2

st x

nd x

rd x

4 5 2 180x x x

25 , 100 , 55

5 7 180x 7 175x

25x

Classwork

(if time permits):

17 – 19, 21/70

Get ready for a “Small Quiz” to be written

on your grade sheet.

Solve:

Quiz. Copy the problems and write the answer.

Put your grade paper on the front of your row, quiz side down.

3 5 3 32. 10

4 8 8 4x x

1. ( 4)( 3) 0x x

THE END