# Help! Problem solving math problem?

The Concordia Theatre contains 500 seats and the ticket prices for a recent play were $43 for adults and $28 for children. For one matinee, if the total proceeds were $16,805, how many children and how many adult tickets were sold?

### 1 Answer

- AlLv 78 years ago
You need two equations. Let A = Adults and C = children

So total adults + total children = 500, therefore

A + C = 500 The second equation involves cost $43 per Adult and $28 for Children and the total money is 16805. So second equation is 43A + 28C = 16805

A + C = 500

43A + 28C = 16805

Rearrange the 1st equation to solve for A. A = 500 - C and substitute into the second equation.

43(500 - C) + 28C = 16805 Simplify to get

21500 - 43C + 28C = 16805 simplify further

-15C = -4695 and C = 313 so you had 313 children

Adults would be 500 - 313 or 187