Worked-out Problems

Chapter 3 continued
22. A;
z
12 24
z
12 p 12 p 24
12
z 288
23. H; Let x amount you spent.
Beginning amount Amount spent Amount left over
42.6 x 3.33
42.6 3.33 x 3.33 3.33
39.27 x
24. B; 3y 14.7
3
y
3
1 4. 7
3
y 4.9
25. A square has 4 sides of equal lengths. You can express the
perimeter P as P 4s.
P 4s
84 4s
8 4
4 s
4 4
21 s
The side length of the square is 21 meters.
26. a. 1500 250 1750
The original price of the TV at store A is $1750.
b. Store A offers a better deal. After the rebate and
delivery, the total price at store A is $1550. Store B
has no rebate. Their price is 1750 75 $1675.
27. B; 2x 7 25
2x 7 7 25 7
2x 18
2x
18
2
2
x 9
28. G; Let x price of breadsticks.
Total cost Cost of pizza Cost of breadsticks
12.99 7.99 2x
12.99 7.99 7.99 2x 7.99
5 2x
5 2 2 x
2
2.5 x
29. B; 15 2(w 5) 11
15 2w 10 11
2w 5 11
2w 5 5 11 5
2w 6
2w
6
2
2
w 3
112 Pre-Algebra
Chapter 3 Worked-Out Solution Key
30. F; A lw
28 4(3x 4)
28 12x 16
28 16 12x 16 16
12 12x
1 2
1 2x
12
12
1 x
31. D; 2(x 1) 3x (x 2)
2x 2 3x x 2
2x 2 2x 2
Every number is a solution.
32. G
33. C; Let x the amount you can spend.
Total
cost
≥
25 ≥ x 13.35
25 13.35 ≥ x 13.35 13.35
11.65 ≥ x
h
34. H; ≥ 14 7
h
7 p ≤ 7 p 14
7
h ≤ 98
35. A; 4s < 42
4(11) ? < 42
44 > 42
So, 11 is not a solution.
36. F; 4 6x ≥ 8 4x
4 6x 4x ≥ 8 4x 4x
4 2x ≥ 8
4 2x 4 ≥ 8 4
2x ≥ 12
2 x
≥ 12
2 2
x ≥ 6
37. First use the distributive property. Then collect like terms
and isolate the variable.
15z 12 3(14 3z) 12
15z 12 42 9z 12
15z 12 30 9z
15z 12 9z 30 9z 9z
6z 12 30
6z 12 12 30 12
6z 42
6 z
4 2
6 6
z 7
Amount of
your dinner
Amount of
friend’s dinner
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