Elena B. answered 12/05/14
GMAT/GRE, SAT/ACT, Advanced Math - College Counseling
Profit after selling 9 costumes is $62.50 so we can get the price at which each costume is sold.
if Price/costume= p then 9p-50 = 62.50, then p=$12.50
Now the function P(c) represents profits as a function of c, # of costumes sold so :
P(c) = 12.5c - 50
This is a line with positive slope = 12.50 and y-intercept = -50 (initial cost of the booth)
c-intercepts = 4 (solving this equation for P(c) = 0)
Therefore, c-intercepts represents the break even point meaning that the Drama Club will start making a profit with the fifth costume sold.