162 Chapter 3 Solving Equations Answers 3. The number is 7. 4. 3x 5. 7d 6. x 8 Translating Sentences to Mathematical Equations Example 3 Two times the sum of a number and 8 equals 38. Find the number. Solution: Step 1: Read the problem completely. Let x represent the number. Step 2: Label the unknown. Two times the sum of a number and 8 equals 38. two times equals 38 Step 3: Write the equation in words. Step 4: Translate to a mathematical • • 2 1x 82 38 the sum of a equation. number and 8 Step 5: Solve the equation. Clear parentheses. Subtract 16 from both sides. Simplify. Divide both sides by 2. ∂ 21x 82 38 2x 16 38 2x 16 16 38 16 2x 22 2x 2 22 2 x 11 The number is 11. Step 6: Interpret the answer in words. 3. Applications of Linear Equations In Example 4, we practice representing quantities within a word problem by using variables. Example 4 Representing Quantities Algebraically a. Kathleen works twice as many hours in one week as Kevin. If Kevin works for h hours, write an expression representing the number of hours that Kathleen works. b. At a carnival, rides cost $3 each. If Alicia takes n rides during the day, write an expression for the total cost. c. Josie made $430 less during one week than her friend Annie made. If Annie made D dollars, write an expression for the amount that Josie made. Solution: a. Let h represent the number of hours that Kevin works. Kathleen works twice as many hours as Kevin. 2h is the number of hours that Kathleen works. Example 4 Skill Practice 3. 8 added to twice a number is 22. Find the number. Skill Practice 4. Tasha ate three times as many M&Ms as her friend Kate. If Kate ate x M&Ms, write an expression for the number that Tasha ate. 5. Casey bought seven books from a sale rack. If the books cost d dollars each, write an expression for the total cost. 6. One week Kim worked 8 hr more than her friend Tom. If Tom worked x hours, write an expression for the number of hours that Kim worked. 5 Avoiding Mistakes The sum 1x 82 must be enclosed in parentheses so that the entire sum is multiplied by 2. Avoiding Mistakes To check the answer to Example 3, we have: The sum of 11 and 8 is 19. Twice this amount gives 38 as expected.
miller_prealgebra_2e_ch1_3
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