Section 2.5 Order of Operations and Algebraic Expressions 117 Using Algebraic Expressions in Applications Example 5 a. At a discount CD store, each CD costs $8. Suppose n is the number of CDs that a customer buys. Write an expression that represents the cost for n CDs. b. The length of a rectangle is 5 in. longer than the width w. Write an expression that represents the length of the rectangle. Solution: a. The cost of 1 CD is 8(1) dollars. The cost of 2 CDs is 8(2) dollars. The cost of 3 CDs is 8(3) dollars. The cost of n CDs is 8(n) dollars or simply 8n dollars. b. The length of a rectangle is 5 in. more than the width. The phrase “more than” implies addition. Thus, the length (in inches) is represented by w w 5 length w 5 Translating to an Algebraic Expression Example 6 Write each phrase as an algebraic expression. a. The product of 6 and x b. p subtracted from 7 c. The quotient of c and d d. Twice the sum of y and 4 Solution: a. The product of 6 and x: 6x b. p subtracted from 7: 7 p c. The quotient of c and d: d. Twice the sum of y and 4: 21y 42 c d 3. Evaluating Algebraic Expressions The value of an algebraic expression depends on the values of the variables within the expression. Answers w 6. 7p 7. L 44 8. 4 9. x 11 10. 9p 11. 41m n2 From this pattern, we see that the total cost is the cost per CD times the number of CDs. “Product” implies multiplication. To subtract p from 7, we must “start” with 7 and then perform the subtraction. “Quotient” implies division. The word “twice the sum” implies that we multiply the sum by 2. The sum must be enclosed in parentheses so that the entire quantity is doubled. Skill Practice 6. Smoked turkey costs $7 per pound.Write an expression that represents the cost of p pounds of turkey. 7. The width of a basketball court is 44 ft shorter than its length L.Write an expression that represents the width. Skill Practice Write each phrase as an algebraic expression. 8. The quotient of w and 4 9. 11 subtracted from x 10. The product of 9 and p 11. Four times the sum of m and n
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