Worked-out Problems

Chapter 3 continued
38. Let x number of tickets.
a. DJ Decoration Cost of Number
< p
cost cost tickets of tickets
125 47.5 < 4.5x
172.5 < 4.5x
17 2.5
4.5
< 4 . 5x
4
. 5
38 1 3 < x
You must sell at least 39 tickets for a profit.
b. DJ Decoration Desired Cost of Number
≤ p
cost cost profit tickets of tickets
125 47.5 300 ≤ 4.5x
472.5 ≤ 4.5x
47 2.5
4.5
≤ 4 . 5x
4
. 5
105 ≤ x
You must sell at least 105 tickets for a profit of at
least $300.
c. Raising the ticket price to $5.00 will lower the amount
of tickets needed to be sold in parts (a) and (b).
Sample answer: The tickets are more expensive, so
you need to sell fewer tickets to have the same income.
For part (a), you would start making a profit when
5x > 125 47.5, or when 35 tickets are sold. For part
(b), you would start making a profit of at least $300
when 5x ≥ 125 47.5 300, or when 95 or more
tickets are sold.
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Chapter 3
Pre-Algebra 113
Worked-Out Solution Key