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.

Required:
What is the maximum number of adults who could attend if the event fills the venue to capacity?

Answer 1

75 adults

Explanation:

Let

x = number of children

y = number of adults

x + y = 200 (1)

9x + 18y = 2,475 (2)

From (1)

x = 200 - y

9x + 18y = 2,475

9(200 - y) + 18y = 2,475

1800 - 9y + 18y = 2,475

- 9y + 18y = 2,475 - 1800

9y = 675

y = 675/ 9

y = 75 adults

Substitute y = 75 into (1)

x + y = 200

x + 75 = 200

x = 200 - 75

x = 125 children

The maximum number of adults who could attend if the event fills the venue to capacity is 75