6.3 Applications of Algebra 315 of pineapple juice. We then can write expressions for the number of ounces of ginger ale and the number of ounces of orange juice in terms of the variable x. Let x x x number of ounces of pineapple juice 2 number of ounces of ginger ale 5 number of ounces of orange juice = = = Next, the sum of these amounts must equal 256 ounces. x x x 2 5 256 + + = x8 256 = x 32 = Thus, Casey must mix 32 ounces of pineapple juice, 2(32), or 64 ounces of ginger ale, and 5(32), or 160 ounces of orange juice. To check this answer, we note that 32 64 160 256. + + = 7 Now try Exercise 33 Example 3 Dimensions of a Sandbox Javier is building a rectangular sandbox for his children. He has 34 ft of wood to use for the perimeter of the sandbox. What should be the dimensions of the sandbox if he wants the length to be 3 ft greater than the width? Solution The formula for determining the perimeter of a rectangle is P l w 2 2 , = + where P is the perimeter, l is the length, and w is the width. The length is 3 ft more than the width; therefore, l w 3. = + A diagram, such as the one below, is often helpful in solving problems of this type. l 5 w 1 3 w The perimeter of the sandbox, P, is 34 ft. Substitute the known quantities in the formula. = + = + + = + + = + = = P l w w w w w w w w 2 2 34 2( 3) 2 34 2 6 2 34 4 6 28 4 7 The width of the sandbox is 7 ft and the length of the sandbox is 7 3 10 ft. + = 7 Now try Exercise 35 Our next example involves percent and calculating sales tax—two concepts important for our financial literacy.
RkJQdWJsaXNoZXIy NjM5ODQ=