Question 1057158: the local amateur football club spent $675 on tickets to a professional football game. if the club bought three fewer fifteen dollar tckets than four-fifths the number of twelve dollar tickets, how many tickets of each type did the club buy?
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! Let x represent the number of $12 tickets purchased.
Then, the number of $15 tickets is "three fewer ... than four-fifths the number" of $12 tickets.
The number of $15 tickets can then be represented as:
(4/5)x - 3
The amount collected from the sale of $12 tickets is 12 * x = 12x.
The amount collected from the sale of $15 tickets is 15 * [(4/5)x - 3] = 12x - 45.
Together, these amounts must add up to the total ticket sales of $675, which
gives the following equation:
12x + (12x - 45) = 675
Collecting like terms on the left side gives:
24x - 45 = 675
Adding 45 to both sides then gives:
24x = 720
Dividing both sides by 24 then leaves:
x = 30
This is the number of $12 tickets. You can then substitute x = 30 into "(4/5)x - 3"
to get the number of $15 tickets.
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