Question 221208
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 = {{{300P - (250 + 150P)}}}


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 = {{{300P - 550}}}


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 - 250 - 150P > 300P - 550


300P - 150P - 300P > - 550 + 250


- 150P > - 300


P < {{{(-300)/-150}}}, or P < {{{2}}} ----- 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 < ${{{highlight_green(2)}}} each.