A theater charges $25 for adults and $15 for children. When the price of a child's ticket increases to $18 next year, the cost for a dance club to attend the theater will increase from $450 to $480. Write and solve a system of equations to find how many adults are in the dance club.

Given:

tickets for adults - 25

tickets for kids - 15

initial cost - 450

increase in tickets for kids to - 18

cost after increase - 480

let x be number of adults and y be number of kids

25x + 15y = 450

25x + 18y = 480

subtraction:

25x + 15y = 450

-25x - 18y = - 480

0 - 3y = - 30

y = - 30/-3

y = 10

There are 10 kids.

25x + 15y = 450

25x + 15 (10) = 450

25x + 150 = 450

25x = 450 - 150

25x = 300

x = 300/25

x = 12

There are 12 adults.

All in all there are 12 adults and 10 kids.

to check:

25x + 15y = 450

25 (12) + 15 (10) = 450

300 + 150 = 450

450 = 450

25x + 18y = 480

25 (12) + 18 (10) = 480

300 + 180 = 480

480 = 480