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Write an Equation

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

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Write an Equation

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  1. 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 Equation 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

  2. amount of amount of total 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 Write an Equation (continued) linseed oil turpentine ratio 1 : 3 unknown amounts 1a : 3a 5-3

  3. a + 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

  4. 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 Equation 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

  5. Wordsamount 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

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

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

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