Worked-out Problems

Chapter 3 continued
33. Sample answer: You and a friend decide to start a dogwalking
service. In one day you walk 11 dogs and earn
$5 in tips. Your friend walks 8 dogs and earns $23 in tips.
If you both earn the same amount of money, what was the
cost to walk a dog?
Let x the cost to walk a dog.
Dogs
you
walked
Dogs
Cost to
Cost to
Your your
p walk a p walk a
tips friend
dog
dog
walked
11x 5 8x 23
11x 5 8x 8x 23 8x
3x 5 23
3x 5 5 23 5
3x 18
3 x
1 8
3 3
x 6
$6 was charged to walk a dog.
34. 3x 7 8 6(x 2)
3x 7 8 6x 12
3x 7 6x 20
3x 7 3x 6x 20 3x
7 3x 20
7 20 3x 20 20
27 3x
27 3x
3 3
9 x
Check: 3x 7 8 6(x 2)
3(9) 7 8 6(9 2)
34 34 ✓
35. 13y 19 6(9 y) 14
13y 19 54 6y 14
13y 19 6y 68
13y 19 6y 6y 68 6y
7y 19 68
7y 19 19 68 19
7y 49
7 y
4 9
7 7
y 7
Check: 13y 19 6(9 y) 14
13(7) 19 6(9 7) 14
110 110 ✓
Your
friend’s
tips
36. 8(z 4) 5(13 z)
8z 32 65 5z
8z 32 5z 65 5z 5z
3z 32 65
3z 32 32 65 32
3z 33
3 z
3 3
3 3
z 11
Check: 8(z 4) 5(13 z)
8(11 4) 5(13 11)
120 120 ✓
37. 8a 2(a 5) 2(a 1)
8a 2a 10 2a 2
6a 10 2a 2
6a 10 2a 2a 2 2a
4a 10 2
4a 10 10 2 10
4a 8
4 a
8 4 4
a 2
Check: 8a 2(a 5) 2(a 1)
8(2) 2(2 5) 2(2 1)
2 2 ✓
38. a. The triangle has the greater side length. Sample answer:
The triangle has the greater side length because the
sum of 3 of its sides is equal to the sum of 4 of the
square’s sides.
b. 3x 2x 3
3x 2x 2x 3 2x
x 3
3x 3(3) 9
The side length of the square is 9 units.
5x 3 5(3) 3 15 3 12
The side length of the triangle is 12 units.
c. P 4s 4(9) 36
The perimeter of the square is 36 units.
P 3s 3(12) 36
The perimeter of the triangle is 36 units.
86 Pre-Algebra
Chapter 3 Worked-Out Solution Key
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