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Write an Equation

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The total amount of polish is 10 cups. The ratio of linseed oil to turpentine is 1 : 3. Find the amount of linseed oil needed for 10 cups of polish.

To find out how much linseed oil you need, set up an equation.

First, use the variable a in a ratio that represents the unknown amounts of

linseed oil and turpentine.

COURSE 3 LESSON 5-3

An old formula for making polish calls for 1 part of boiled linseed oil for every 3 parts of turpentine. How much linseed oil is needed to make 10 cups of the polish?

5-3

amount of amount oftotal amount

linseed oil turpentine of polish

Let 1a = the amount of linseed oil.

Let 3a = the amount of turpentine.

+ =

Words

1a + 3a = 10

Equation

COURSE 3 LESSON 5-3

(continued)

linseed oilturpentine

ratio 1: 3

unknown amounts 1a: 3a

5-3

a + 3a = 10Write the equation.

4a = 10Combine like terms.

= Divide each side by 4.

a = 2.5Simplify.

1(2.5) = 2.5Substitute 2.5 for a in 1a.

4a

4

10

4

The amount of turpentine needed is 3(2.5) = 7.5. Since 7.5 + 2.5 = 10, the answer is correct.

The amount of linseed oil needed is 2.5 cups.

COURSE 3 LESSON 5-3

(continued)

5-3

A gallon is 128 oz. The ratio of the paint colors is 3 to 5 to 8. Find how many ounces of each color are needed.

Writing an equation will help you solve the problem. The ratio of red

to blue to white paint is 3 : 5 : 8. So 3p represents red, 5p represents blue,

and 8p represents white.

COURSE 3 LESSON 5-3

To paint a cabinet purple, you are going to mix red, blue, and white paint in a ratio of 3 : 5 : 8. To make a gallon of paint, how many ounces of each color will you use?

5-3

Wordsamount amount amount total amount of

of red of blue of white paint needed

+ + =

3p + 5p + 8p = 128

Equation

16p = 128Combine like terms

= Divide each side by 16.

p = 8Simplify.

128

16

16p

16

COURSE 3 LESSON 5-3

(continued)

5-3

Since 24 + 40 + 64 = 128, the answer is correct.

COURSE 3 LESSON 5-3

(continued)

Substitute 8 for p in the expression for each color.

red: 3(8) = 24 oz blue: 5(8) = 40 oz white: 8(8) = 64 oz

5-3

COURSE 3 LESSON 5-3

Write an equation to solve each problem. Show your equation and your answer.

1.A punch recipe calls for 3.5 qt fruit juice to 2.5 qt soda water. You want 18 qt of punch in all. How much fruit juice do you need?

2.A painter is mixing white, yellow, and red in a ratio of 4 : 3 : 1. He needs 2 gallons. If there are 128 ounces in a gallon, how much white is needed?

3.5x + 2.5x = 18; 10.5 qt

4p + 3p + p = 2(128); 128 oz, or 1 gal

5-3