1. Write an Equation 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? 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. 5-3

2. Write an Equation COURSE 3 LESSON 5-3 (continued) linseed oilturpentine ratio 1: 3 unknown amounts 1a: 3a 5-3 + = Equation 1a + 3a = 10 Words amount of amount oftotal amount linseed oil turpentine of polish Let 1a = the amount of linseed oil. Let 3a = the amount of turpentine.

3. Write an Equation COURSE 3 LESSON 5-3 (continued) The amount of turpentine needed is 3(2.5) = 7.5. Since 7.5 + 2.5 = 10, the answer is correct. 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. 4a44a4 10 4 The amount of linseed oil needed is 2.5 cups. 5-3

4. Write an Equation 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? 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. 5-3

5. Write an Equation COURSE 3 LESSON 5-3 (continued) 16p = 128Combine like terms = Divide each side by 16. p = 8Simplify. 16p 16 128 16 5-3 Equation + + = 3p + 5p + 8p = 128 Words amount amount amount total amount of of red of blue of white paint needed

6. Write an Equation COURSE 3 LESSON 5-3 (continued) Since 24 + 40 + 64 = 128, the answer is correct. 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

7. Write an Equation 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? COURSE 3 LESSON 5-3 3.5x + 2.5x = 18; 10.5 qt 4p + 3p + p = 2(128); 128 oz, or 1 gal 5-3