Worked-out Problems

Chapter 3 continued
5. 12 2m 5 1
2m 17 1
2m 17 17 1 17
2m 18
2
m
2
18
2
m 9
Check: 12 2m 5 1
12 2(9) 5 1
1 1 ✓
6. 6y 4 11y 16
5y 4 16
5y 4 4 16 4
5y 20
5 y
20
5 5
y 4
Check: 6y 4 11y 16
6(4) 4 11(4) 16
16 16 ✓
7. 3(8 a) 12
24 3a 12
24 3a 24 12 24
3a 12
3
a
3
12
3
a 4
Check: 3(8 a) 12
3(8 4) 12
12 12 ✓
8. 6(3x 15) 18
18x 90 18
18x 90 90 18 90
18x 108
18x
108
18
18
x 6
Check: 6(3x 15) 18
5[3(6) 15] 18
18 18 ✓
9. 5t 5 5t 4
5t 5 5t 5t 4 5t
5 4
No solution
10. 2n 6 8n 14
2n 6 8n 8n 14 8n
10n 6 14
10n 6 6 14 6
10n 20
1 0n
2 0
10
10
n 2
Check: 2n 6 8n 4
2(2) 6 8(2) 14
2 2 ✓
11. 8b 4 4(b 7)
8b 4 4b 28
8b 4 4b 4b 28 4b
4b 4 28
4b 4 4 28 4
4b 32
4 b
32
4 4
b 8
Check: 8b 4 4(b 7)
8(8) 4 4(8 7)
60 60 ✓
12. 16p 8 2(8p 4)
16p 8 16p 8
Every number is a solution.
13. Let x the cost of an adult movie ticket.
Cost of Number Cost of Number
Total
child’s p of adult’s p of
cost
ticket children ticket adults
Number of
Cost of
p boxes of
popcorn
popcorn
26.50 3.50(2) x(2) 2.50(3)
26.50 7 2x 7.50
26.50 2x 14.50
26.50 14.50 2x 14.50 14.50
12 2x
1 2
2 x
2 2
6 x
An adult movie ticket costs $6.
14. Let x the temperature in C at which ocean
water freezes.
x ≤ 1.9
2 1.8 1.6 1.4 1.2 1
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Chapter 3
Pre-Algebra 107
Worked-Out Solution Key