algebra 2 help asap

Question

The members of the Drama Club sold their old costumes in a booth at the school craft fair. Their profit was the difference between the amount of money they made selling the costumes and the cost of the booth. The cost of the booth was $50 and each of the costumes was sold for the same price. After the members of the Drama Club had sold 9 costumes, they had made a profit of $62.50. The function p represents the Drama Club's profit as a function of c, the number of costumes they sold. What does the c-intercept of the function represent?

Answer 1

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.