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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

Write an EquationAn 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 of total amount oil to turpentine is 1 : 3. Find the amount of linseed oil needed for 10 cups of polish.

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

Write an Equation(continued)

linseed oil turpentine

ratio 1 : 3

unknown amounts 1a : 3a

5-3

a oil to turpentine is 1 : 3. Find the amount of linseed oil needed for 10 cups of polish. + 3a = 10 Write the equation.

4a = 10 Combine like terms.

= Divide each side by 4.

a = 2.5 Simplify.

1(2.5) = 2.5 Substitute 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

Write an Equation(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

Write an EquationTo 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

Words to 8. Find how many ounces of each color are needed.amount amount amount total amount of

of red of blue of white paint needed

+ + =

3p + 5p + 8p = 128

Equation

16p = 128 Combine like terms

= Divide each side by 16.

p = 8 Simplify.

128

16

16p

16

COURSE 3 LESSON 5-3

Write an Equation(continued)

5-3

Since 24 + 40 + 64 = 128, the answer is correct. to 8. Find how many ounces of each color are needed.

COURSE 3 LESSON 5-3

Write an Equation(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 to 8. Find how many ounces of each color are needed.

Write an EquationWrite 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

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