SOLUTION: 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

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): You can put this solution on YOUR website!
Let = price/ticket in dollars to charge
Let = profit for school
Write 2 equations, 1 for each band
(1)
(1)
(1)
(1)
and
(2)
If the profits from the 2 bands were equal,

If the ticket price were $1.99
(1)
(1)
(1)
and
(2)
(2)
(2)
1st band is more profitable
If the ticket price were $2.01
(1)
(1)
(1)
and
(2)
(2)
(2)
Band (2) becomes more profitable for the
school, when the ticket price goes over
$2.00, so the ticket price has to be
under $2.00 to make more profit from 1st band

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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