I got stuck partway through a problem!

Last year, Central High's yearbook costs $75 and only 500 were sold. A really smart math student realized that for every $5 in reduction in price, 100 more students will buy yearbooks. What price should be charged so that the school maximizes revenue from yearbook sales?

I know that if x = cost of a yearbook and y = the number sold then xy = R, (R= the revenue). Then I know that for n number of reductions in price the yearbook will cost 75-5n and 500+100n students will buy the yearbook. And then I'm stuck ;A;

Question

I got stuck partway through a problem!

Last year, Central High's yearbook costs $75 and only 500 were sold. A really smart math student realized that for every $5 in reduction in price, 100 more students will buy yearbooks. What price should be charged so that the school maximizes revenue from yearbook sales?

I know that if x = cost of a yearbook and y = the number sold then xy = R, (R= the revenue). Then I know that for n number of reductions in price the yearbook will cost 75-5n and 500+100n students will buy the yearbook. And then I'm stuck ;A;

jim_thompson5910 · Answer

Let

x = number of reductions of $5 in the price of the yearbook
y = total revenue from selling 500+100x books


total revenue = (price per book)*(number of books)
y = (75-5x)*(500+100x)
y = 75*(500+100x) - 5x*(500+100x)
y = 75*(500)+75*(100x) - 5x*(500) - 5x*(100x)
y = 37500 + 7500x - 2500x - 500x^2
y = -500x^2 + 5000x + 37500


Do you see where to go from here?

cocoacat · Answer

Ohmygosh thank you so much!! I totally see what to do now! You're the best!