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Back to Lesson 8-6 Name Name 6-5B 8-5B page 2 Questions on SPUR Objectives See pages 549–551 for objectives. SKILLS Objective B 37% 9. Carlos had a 10% off coupon and spent it on a computer game that was marked down 30%. What was his total discount? 8-6A Lesson Master In 1−3, solve mentally. 10. After a discount of 20%, the dress Sharon wanted was $85. What was the original price of the dress? $106.25 1. 6x = 18 2. 48 = 8m 3 x= 11. A collectible comic book worth $40 two years ago gained 15% in value the next year, but then lost 15% in value this year. What is it worth now? $39.10 12. A piece of property increased in value by 14% in one year and by 10% in the next year. What was the percent of increase over the two years? 4. 15q = 50 25.4% 14. The price of an item in a store is reduced by 50%. Then the price is reduced by another 50%. What is the total percent change as a result of the two discounts? 7.5 d= In 4−6, use the Multiplication Property of Equality to solve the equation. Check your answer. 5. 4.2 = 0.14r q = 3 _3 2.6% increase in value 13. A piece of property increased in value by 14% in one year and decreased in value by 10% the next year. What was the percent change in value over the two years? 3. 10d = 75 6 m= 1 6. 75% of s = 15 r = 30 PROPERTIES s = 20 Objective E 7. What does the Multiplication Property of Equality allow you to do? Why is this procedure useful? 75% 15. Explain why the cost of an item discounted 20% can be calculated by multiplying the original price by 0.8. Let P be the original price. Then 0.2P is the discount amount and P - 0.2P is the cost. Using the Distributive Property, P - 0.2P = 0.8P. 8. It allows you to multiply both sides of an equation by the same number. It can be used to solve equation involving multiplication. 30y Fill in the blank. If x = 3y, then 10x = . 9. To solve 60 = 1.5m, what should be done to both sides of the equation? 1 Multiply sides by ___ 1.5 . USES Objective G 16. Explain why the cost of an item discounted 20% and then taxed 8% can be calculated by multiplying the original price by 0.864. Let P be the original price. Then 0.2P is the discount amount and P - 0.2P = 0.8P is the cost before taxes. The cost with 8% tax is 1.08(0.8P) = 0.864P In 10−12, write an equation of the form ax = b for each situation, and then solve the equation. 10. A rectangle has area 475 ft2 and width 25 ft. Find its length. 25 · L = 475 equation: L = 19 answer: 11. At Liddle Middle School, 32% of the students are 7th graders. If there are 112 students in the seventh grade, how many students are in the school? 0.32 · s = 112 equation: s = 350 answer: 12. At a speed of 17 miles per second, approximately how many hours would it take a spaceship to travel to the moon, a distance of 239,000 miles? 17 · t = 239,000; t ≈ 14,059 seconds; 60 · 60 · h = 14,059 equation: Transition Mathematics 392 Transition Mathematics UCSMP_SMP08_NL_TM2_TR2_C08_378-4392 392 UCSMP_SMP08_NL_TM2_TR2_C08_378-4393 6/6/07 4:09:32 PM 393 6/6/07 4:09:32 PM Name 8-6B Lesson Master SKILLS 8-6B Objective B: Solve and check equations of the form ax = b page 2 PROPERTIES Objective E: Recognize and use the Multiplication Properties of Equality and Inequality. and ax + b = c. 21. Give an instance of the Multiplication Property of Equality. In 1−9, give the reciprocal of each expression. 1. −5 − _15 4. −1.8 −5 __ 2. − __49 −1 __ 1 3. __6 − _94 6. −2 __34 5. 1 1 9 7. −e 1 8. __e e 6 Tom multiplied both sides by ; Tim multiplied both sides by 4; They both got x = −8 as the answer. −4 __ 11 −m 9. ___ n e n __ 23. Multiple choice. What should be done to the equation __45 y = 20 to solve for y? −m 10. 3x = 42 11. 4t = −34 12. −d = 40.9 13. −9y = 54 14. −104 = −4r −8 15. ___ 5 x = 96 16. −7.4k = 111 17. −9 = −25g x = 14 d = −40.9 r = 26 k = −15 5 −1 __ 18. ___ 8 q = 24 −5 _2 q = __ 3 or −1 3 20. 4d + 2d = −16 d = −2 _23 t = −8.5 y = −6 x = −60 9 g = __ 25 or 0.36 −4 B Multiply both sides by ___ . 5 C Divide both sides by __54 . −4 D Divide both sides by ___ . 5 USES Objective G: Find unknowns in real situations involving multiplication. In 24−27, write an equation of the form ax = b for each situation, and then solve the equation. 24. Mrs. Doherty wants to make a 150-square foot rectangular vegetable garden along the side of her garage. If the garage is 20 feet long, how wide should the garden be? answer 25. Four-fifths of a number is 212. What is the number? _4 n = 212 5 n = 265 equation REVIEW answer Chapter 2, Objective C In 26−31, translate into a mathematical expression. 12 - 8 8 < 12 _1 6 more than half a number 2 n + 6 8 - 12 (11)(17) 6 decreased by twice a number 6 - 2n 26. twelve less 8 27. twelve less than 8 28. Eight is less than 12. 29. the product of 11 and 17 30. 31. Transition Mathematics UCSMP_SMP08_NL_TM2_TR2_C08_378-4394 394 x = 7.5 ft 20x = 150 equation x = −0.1425 t = 0.2 A A Multiply both sides by __54 . 19. 3.2x = −0.456 1 21. __2 t - 4t = −0.7 Sample: If 2p = 5, then 10p = 25. 22. Given the equation __34 x = −6, Tom wrote __14 x = −2, and Tim wrote 3x = −24. Show why both Tim and Tom are correct, and solve the equation. _1 3 In 10−19, solve and check. A52 393 Transition Mathematics UCSMP_SMP08_NL_TM2_TR2_C08_378-4395 6/6/07 4:09:32 PM 395 Copyright © Wright Group/McGraw-Hill Name 394 h ≈ 3.9 answer: 395 6/6/07 4:09:33 PM Transition Mathematics SMP08_TM2_TR2_C07-12_A43-A82.indA52 A52 6/6/07 5:40:16 PM