Worked-out Problems

Chapter 3 continued
27. Let x the number of times you pay for the tolls.
Toll cost Times Cost to
Times
Toll cost
without p you pay replace p you pay
with tag
tag tolls tag
tolls
3x 24 1.5x
3x 1.5x 24 1.5x 1.5x
1.5x 24
1 . 5x
24
1.
5 1 . 5
x 16
You will have to use the tag 16 times for the cost to be
the same.
28. 4x 36 5x
4x 5x 36 5x 5x
9x 36
9 x
3 6
9 9
x 4
4x 4(4) 16
P 4s 4(16) 64
The perimeter of the square is 64 units.
29. 12x 7x 30
12x 7x 7x 30 7x
5x 30
5 x
3 0
5 5
x 6
12x 12(6) 72
P 4s 4(72) 288
The perimeter of the square is 288 units.
30. 9x 5x 32
9x 5x 5x 32 5x
4x 32
4 x
3 2
4 4
x 8
9x 9(8) 72
P 4s 4(72) 288
The perimeter of the square is 288 units.
31. a. 700 60x
b. 400 60x
c. 700 60x 400 60x
700 60x 60x 400 60x 60x
700 400 120x
700 400 400 120x 400
300 120x
3 00
1 20x
120
120
2.5 x
In 2.5 hours, you will be exactly halfway between
Houston and home.
d. 700 45x 400 45x
700 45x 45x 400 45x 45x
700 400 90x
700 400 400 90x 400
300 90x
3 00
9 0x
90
90
3 1 3 x
You will drive 3 1 3 hours before you are exactly
halfway between Houston and home.
32. Let x the batches of pasta you make.
Cost of
purchased
pasta
Cost of Cost to
Batches
p pasta make p
of pasta
machine pasta
0.99x 33 0.33x
0.99x 0.33x 33 0.33x 0.33x
0.66x 33
0 . 66x
33
0.
66
0 .66
x 50
Batches
of pasta
You will need to make 50 batches of pasta for the costs to
be equal.
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Chapter 3
Pre-Algebra 85
Worked-Out Solution Key