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Two-Step Equations: Mechanic's Bill Calculation

Learn how to solve two-step equations using inverse operations. Calculate the number of hours a mechanic worked on a car based on the total bill.

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Two-Step Equations: Mechanic's Bill Calculation

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  1. y9 Lesson 23 Warm Up Solve. 1.x + 12 = 35 2. 8x = 120 3.= 7 4. –34 = y + 56 x = 23 x = 15 y = 63 y = –90

  2. Lesson 23 Learn to solve two-step equations.

  3. Lesson 23 Sometimes more than one inverse operation is needed to solve an equation. Before solving, ask yourself, “What is being done to the variable, and in what order?” Then work backward to undo the operations.

  4. Lesson 23 The mechanic’s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car?

  5. 1 Understand the Problem Lesson 23 List the important information: The answer is the number of hours the mechanic worked on your car. • The parts cost $275. • The labor cost $35 per hour. • The total bill was $850. Let h represent the hours the mechanic worked. Total bill = Parts + Labor 850 = 275 + 35h

  6. 2 Make a Plan Lesson 23 Think: First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 275 from both sides of the equation, and then divide both sides of the new equation by 35.

  7. 3 Solve 575 35h = 3535 Lesson 23 850 = 275 + 35h –275–275Step 1: Subtract to undo the addition. 575 = 35h Step 2: Divide to undo multiplication. 16.4 h The mechanic worked for about 16.4 hours on your car.

  8. 4 Look Back Hours Labor Parts Total Cost 13 455 $275 $730 14 490 $275 $765 15 525 $275 $800 16 560 $275 $835 17 595 $275 $870 Lesson 23 You can use a table to decide whether your answer is reasonable. 16.4 hours is a reasonable answer.

  9. n3 n3 + 7 – 7= 22 – 7 n3 3 = 3  15 Lesson 23 Solve + 7 = 22. Work backward to isolate the variable. Think: First the variable is divided by 3, and then 7is added. To isolate the variable, subtract 7, and then multiply by 3. Subtract 7 from both sides. Multiply both sides by 3. n = 45

  10. y – 4 y – 4 3 3 Lesson 23 Solve = 9. Work backward to isolate the variable. Think: First the variable is being subtracted by 4 and thenis divided by 3. To isolate the variable, multiply by 3 and then add 4. (3)(3) = 9 Multiply both sides by 3. Y – 4 = 27 +4 +4 y = 31 Add 4 to both sides.

  11. n4 n4 + 8 – 8= 18 – 8 n4 4 = 4  10 Lesson 23 Solve + 8 = 18. Work backward to isolate the variable. Think: First the variable is divided by 4, and then 8is added. To isolate the variable, subtract 8, and then multiply by 4. Subtract 8 from both sides. Multiply both sides by 4. n = 40

  12. y – 7 2 y – 7 = 7 2 y – 7 (2) (2)‏ = 7 2 Lesson 23 Solve = 7. Multiply both sides of the equation by the denominator. Multiply both sides by the denominator. y – 7 = 14 + 7+ 7Add to undo subtraction. y = 21

  13. Lesson 23 Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  14. x –9 Lesson 23 Solve. – 3 = 10 3. –8.3 = –3.5x + 13.4 3. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1014, how many months will the contract last? x = –117 x = 6.2 24

  15. x –9 y + 5 11 Lesson Quiz Solve. 1. – 3 = 10 2. 7y + 25 = –24 3. –8.3 = –3.5x + 13.4 4. = 3 5. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1014, how many months will the contract last? x = –117 y = –7 x = 6.2 y = 28 24

  16. Lesson Quiz for Student Response Systems p-7 1. Solve – 9 = 3. A.p = –84 B.p = –42 C.p = 42 D.p = 84

  17. Lesson Quiz for Student Response Systems 2. Solve 3r + 46 = –29. A.r = –20 B.r = –25 C.r = –30 D.r = –35

  18. Lesson Quiz for Student Response Systems 3. Solve –3.3 = –1.2t + 15.3. A.t = 15.5 B.t = 14 C.t = 12.5 D.t = 10

  19. Lesson Quiz for Student Response Systems v + 7 8 4. Solve = 5. A.v = 31 B.v = 32 C.v = 33 D.v = 34

  20. Lesson Quiz for Student Response Systems 5. The membership fee of a DVD rental store is $15. The cost of renting a DVD is $2. If John pays $27, how many DVDs did he rent? A. 6 DVDs B. 8 DVDs C. 12 DVDs D. 24 DVDs

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