BRING AN EGG CARTON Warm up Week 7 Day One Solve Y 167 49 d h 2 78 b 47m 329 c k32 68 Warm Up Response ID: 1001918
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1. HW # 25- p. 100 # 15-29 all BRING AN EGG CARTON Warm up Week 7, Day OneSolve.Y + 16.7 = -49 d) - h = 2 7.8b) 4.7m = -32.9c) k-3.2 = -6.8
2. Warm Up ResponseSolve.Y + 16.7 = -49 -65.7 d) - h = 2 -15.6 7.8b) 4.7m = -32.9 -7c) k-3.2 = -6.8 -3.6
3. Goals for Today2-8 Two-Step Equations with Rational Numbers
4. Recall that two-step equations contain two operations, and therefore, require two inverse operations to solve. Before solving, ask yourself, “What is being done to the variable, and in what order?” One method to solve the equation is to work backward to undo the operations.
5. The mechanic’s bill to repair Mr. Wong’s car was $653.05. The mechanic charges $45.50 an hour for labor, and the parts that were used cost $443.75. How many hours did the mechanic work on the car? Problem Solving Application
6. Continued1 Understand the ProblemThe answer is the number of hours the mechanic worked on the car.List the important information:Let h represent the hours the mechanic worked. The parts cost $443.75. The labor cost $45.50 per hour. The total bill was $653.05.Total bill = Parts + Labor653.05 = 443.75 + 45.50h
7. Think: First the variable is multiplied by 45.50, and then 443.75 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443.75 from both sides of the equation, and then divide both sides of the new equation by 45.50.2Make a PlanContinued
8. 653.05 = 443.75 + 45.50hSolve3–443.75 –443.75 209.30 = 45.50h4.6 = hThe mechanic worked for 4.6 hours on Mr. Wong’s car.ContinuedSince h is multiplied by 45.50, divide both sides by 45.50.209.30 45.50h 45.50 45.50=Since 443.75 is added to both sides, subtract 443.75 from both sides.
9. You can use a table to decide whether your answer is reasonable.Look Back4ContinuedHoursLaborPartsTotal Cost1$45.50$443.75$489.252$91.00$443.75$534.753$136.50$443.75$580.254$182.00$443.75$625.755$227.50$443.75$671.254.6 hours is a reasonable answer.
10. Example 2 n + 7 = 22 3 n + 7 = 22 3 -7 -7 n = 15 3 3 * n = 15 * 3 3n = 45
11. Example 3Solve = 9.y – 4 3= 9y – 43y – 4 = 27 + 4 + 4 Since 4 is subtracted from y, add 4 to both sides to undo the subtraction.y = 31Multiply both sides by the denominator.Method 2: Multiply both sides of the equation by the denominator.= 9y – 43(3) (3)
12. Example 4 Solve + 8 = 18.N4 + 8 – 8 = 18 – 8n4Since n is divided by 4, multiply both sides by 4.4 = 4 10N4n = 40Method 1: Use fraction operations. + 8 = 18N4Since 8 is added to , subtract 8 from both sides to undo the addition.n4 = 10N4
13. Solve.1. – x – 3 = 102. 7y + 25.68 = –26.123. –8.3 = –3.5x + 13.44. = 3.15. 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 $1032.96, how many months will the contract last?Lesson Quizy = –7.4x = –117x = 6.2y = 29.124 months19y + 5 11
14. 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?EXTRA EXAMPLES: Example 1
15. Check It Out! Example 1 Continued1 Understand the ProblemThe answer is the number of hours the mechanic worked on your car.List the important information:Let h represent the hours the mechanic worked. The parts cost $275. The labor cost $35 per hour. The total bill was $850.Total bill = Parts + Labor 850 = 275 + 35h
16. 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 35.2Make a PlanCheck It Out! Example 1 Continued
17. 850 = 275 + 35hSolve3–275 –275 575 = 35h16.4 hThe mechanic worked for about 16.4 hours on your car.Check It Out! Example 1 Continued575 35h 35 35=Since h is multiplied by 35, divide both sides by 35.Since 275 is added to both sides, subtract 275 from both sides.
18. Look Back4Check It Out! Example 1 ContinuedYou can use a table to decide whether your answer is reasonable.HoursLaborPartsTotal Cost13$455$275$73014$490$275$76515$525$275$80016$560$275$83517$595$275$87016.4 hours is a reasonable answer.