Question

Your school is planning a fundraising dinner. The expense for this event must not exceed $2,475.00. The team organizing the event has calculated that the cost per adult guest will be $18.00 and the cost per child guest will be $9.00. The venue can hold no more than 150 guests.The question is If the event were held in a venue that can accommodate 200 guests, what is the maximum number of adults who could attend if the event fills the venue to capacity? Include a screenshot of your revised graph with your answer.Write a system of inequalities that represents this situation.

Answer 1

Let the number of adults attendees be x, and that of children be y, then
18x + 9y =< 2,475 . . . (1)
x + y = 200 . . . (2)
From (2), y = 200 - x . . . (3)
substituting for y into (1), gives
18x + 9(200 - x) =< 2475
18x + 1800 - 9x =< 2475
9x + 1800 =< 2475
9x =< 2475 - 1800
9x =< 675
x =< 675 / 9
x =< 75.

Therefore, the maximum number of adults who cound attend the event is 75.