Alg 1 CP Midterm Chapter 3 Review Key

Chapter 3 Solve the following equations: 1. a - 17 = -10 a = 7 2. 4l = 52 + m m - 52 = 4l m = 4l + 52 3. c - 2.4 = 1.8 c = 4.2 4. -3/4d = 12 d = -16 5. 1/3a = 8/5 a = 24/5 6. -1.4a = 2.8 a = -2 7. 9c - 5 = 13 9c = 18 c = 2 8. w/7 - 2 = 9 w/7 = 11 w = 77 9. -9 = 11m - 8m -9 = 3m -3 = m 10. 0.4m - 3 = -1 0.4m = 2 m = 5 11. 1.8 = x/4 x = 7.2 12. 38 = 26x - 7x 38 = 19x x = 2 13. 7d - (5 + 12) = 5 7d - 17 = 5 7d = 22 d = 22/7 14. 15m + 4 - 9m = -32 6m + 4 = -32 6m = -36 m = -6 15. 19a - 3(a - 6) = 66 19a - 3a + 18 = 66 16a + 18 = 66 16a = 48 a = 3 16. 1/4(x - 8) = 7 x - 8 = 28 x = 36 17. 6(4r + 2) = 7(3r - 6) 24r + 12 = 21r - 42 3r = -54 r = -18 18. 15 = 4.3n - 2.1(n - 4) 15 = 4.3n - 2.1n + 8.4 15 = 2.2n + 8.4 6.6 = 2.2n 3 = n 19. 1/2(6w + 2) = -w 3w + 1 = -w 4w = -1 w = -1/4 20. t/3 + t/2 = 15 5t/6 = 15 5t = 90 t = 18 21. 8(y - 5) = 6y - 18 8y - 40 = 6y - 18 2y = 22 y = 11 22. 8b + 11 - 3b = 2b + 2 5b + 11 = 2b + 2 3b = -9 b = -3 23. 16p - 4 = 4(2p - 3) 16p - 4 = 8p - 12 8p = -8 p = -1 24. 10d - 6 = 4d - 15 - 3d 10d - 6 = d - 15 9d = -9 d = -1 5. How can you tell if an equation has no solution, one solution or infinitely many solutions? No solution if you get nonsense like 2 = 3. Infinite solutions if you get a true statement like 2   = 2. 8m + 13 = 13 + 8m -8m - 8m 13 = 13 Infinite solutions 6y - 3 = 6y + 8 -6y - 6y -3 = 8 No solution 5t - 2t = 6 + 3t 3t = 6 + 3t -3t - 3t 0 = 6 No solution Write an equation for each problem, then solve. 29. The output of a function is 5 more than 2 times the input. Find the input when the output is 17. y = 2x + 5 17 = 2x + 5 12 = 2x 6 = x 30. A fitness center offers yoga classes for $10 per class and sells yoga mats for $19.95. A person paid a total of $139.95 to the fitness center for yoga classes and   the mat. Find the number of yoga classes the person took.   10x + 19.95 = 139.95 10x = 120 x = 12 classes 31. It takes 70 inches of ribbon to make a bow and wrap the ribbon around the box. The bow takes 32 inches of ribbon. The width of the box is 14 inches. What is the height of the box?   [Image of a box with dimensions] 14 + 14 + x + x + 32 = 70 2x + 60 = 70 2x = 10 x = 5 inches Solve each proportion for the given variable. 32. 3/a = 4/5 4a = 15 a = 15/4 33. 6/7 = 10/w 6w = 70 w = 70/6 = 35/3 34. 8/(x-3) = 4/(2x+5) 8(2x+5) = 4(x-3) 16x + 40 = 4x - 12 12x = -52 x = -52/12 = -13/3 Solve each percent problem. 35. What is 65% of 495? x/495 = 65/100 x = 321.75 36. 45 is 90% of what number? 45/x = 90/100 90x = 4500 x = 50 37. 70% of what number is 56? 56/x = 70/100 70x = 5600 x = 80 38. 3 is 2% of what number? 3/x = 2/100 2x = 300 x = 150