Question

Christine is selling tickets at a museum. She knows that she has sold at least 40 tickets. The adult tickets

cost 14 dollars and the children’s tickets cost 12 dollars. If she knows she has sold no more than $720 worth
of tickets, what are the possible combinations?

Answer 1

Adult tickets cost $80, children ticket cost $40

Explanation:

Given data

let the number of adults be x

and the number of children be y

so

x+y= 40-------------1

The adult tickets

cost 14 dollars and the children’s tickets cost 12 dollars.

14x+ 12y= 720-------2

solve 1 and 2

x+y= 40

14x+ 12y= 720

from 1

x= 40-y

put this in 2 in place of x

14(40-y)+12y= 720

560-14y+12y= 720

collect like terms

-2y= 720-560

-2y= 160

y= -160/2

y= -80

put y= 80 in 1

x+80= 40

x= 40-80

x= -40

Hence Adult tickets cost $80, children ticket cost $40