1. Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
pages 107–110  Exercises
1. a. Let w = width.
b. = w + 3
c. 2w + 2(w + 3) = 30; 6
d. 9 in.
2. 2 in.; 10 in.
3. 9 cm; 18 cm
4. 5 yd; 13 yd
5. C
6. a. Let n = the first integer.
b. 2
c. n + 2
d. n + n + 2 = 118; 58, 60
7. a. Let n = the first integer.
b. 2
c. n + 2
d. n + n + 2 = 56; 27, 29
8. 304, 305, 306
9. –148, –150
10. a. Let t = time for the moving van.
b. t – c.
d. 35t = 50(t – ); t = 2 , 2 – = 1 h h 3 4 3 4 1 2 1 2 3 4 3 4 17 30
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2. Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
12. a. x; 2 – x
b. 22x = 32(2 – x), 1 h
13. a. x; 3 – x
b. 320x = 280(3 – x), 1 h
14. a. x; x – 20
b. 4x + 4(x – 20) = 250,
41 mi/h; mi/h
15. 15mi/h; 20mi/h
16. a. 61
b. They are all multiples
of three. cm
18. x + x x x + 6 = 308;
74, 76, 78, 80 1 4
19. –31, –29, –27
20. a x + x
b ft
c. 3x = 15.5;
10 ft or 10 ft 10 in.
21. 12:30 p.m.
22. a. 45 minutes
b. 3:45
23. 2:30 p.m.
mi/h; 375 mi/h
, 1987, 1988
26. first boat: 20 mi/h;
second boat: 30 mi/h
27. truck: 8 h; train: 6 h
V; 4 12-V
29. Answers may vary.
Sample: Define a
variable to represent
the first integer. Use
this variable to write
expressions for the
other integers. Write
an equation that
describes how the
integers are related.
Solve this equation
to find the integers. 1 4 1 3 2 5 5 6 1 4 1 4
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3. Equations and Problem Solving
ALGEBRA 1 LESSON 2-5
43. –
44. no solution
45. –1 h
47. –12
48. –10
49. 54
50. 3
30. Answers may vary.
Sample: Jeff and Anne
both left school for the
city at the same time.
Jeff drove 35 mi/h and
Anne drove 20 mi/h.
Jeff arrived 1 h before
Anne. How long did
each drive?
31. a. n + n n + 2 = 126;
41, 42, 43
b. Yes; if n is the middle
integer, n – 1 is the
previous integer and
n + 1 is the next integer.
The three integers would
be consecutive.
32. x + 2x – 65 + x – 10 = 165;
60; 55 cm, 60 cm, 50 cm
33. a. h
b. 10:15 A.M.
34. –9, –7, –5, –3, –1
35. A
36. H
37. B
38. G
39. A
40. –2
41. 0 1 3 5 6 5 7 1 2
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