Question 221208: In planning for a school dance, you find that one band will play for $250, plus 50% of the total ticket sales. Another band will play for a flat fee of $550. In order for the first band to produce more profit for the school than the other band, what is the highest price you can charge per ticket, assuming 300 people attend?
i tried setting it up something like .50(250-x)+250>550 x= the price of tickets
but I am not getting the correct answer.
Found 2 solutions by josmiceli, MathTherapy: Answer by josmiceli(19441) (Show Source): Answer by MathTherapy(10551) (Show Source):
You can put this solution on YOUR website! Let price of ticket be P
Then proceeds from sale of 300 tickets = 300P
Since the 1st band wants $250, plus 50% of ticket sales, then the school would have to pay the 1st band 250 + .5(300P), or 250 + 150P, and the profit from using the 1st band =
Since the 2nd band wants a flat fee of $550, then the school would have to pay the 2nd band $550, and the profit from using the 2nd band =
Since we're looking for the 1st band to make more profit for the school than the 2nd band, then we'll have:
300P - 250 - 150P > 300P - 550
300P - 150P - 300P > - 550 + 250
- 150P > - 300
P < , or P < ----- Take note that the inequality changes from > to < when dividing by a negative value
Therefore, in order for the 1st band to make more profit for the school than the 2nd band, the price of 300 tickets should be < $ each.
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