Question

The Family Fine Arts Center charges $ 22 per adult and $ 14 per child under 12

years old for its performances. On a recent weekend evening when 551 people
paid admission, the total receipts were $ 9290. How many who paid were
children under 12 years old?
Let A = number of adult tickets, let C = number of child tickets
1. Using the variables A and C, write a system of linear equations that reflect the
above problem.
2. Solve the system of equations for both A and C.
3. How many tickets sold were for children under 12?

Answer 1

197 adult tickets and 354 child tickets were sold for the event.

Explanation:

Given that the Family Fine Arts Center charges $ 22 per adult and $ 14 per child under 12 years old for its performances, and on a recent weekend evening when 551 people paid admission, the total receipts were $ 9290, to determine how many who paid were children under 12 years old the following calculation must be performed:

22 - 14 = 8

551 x 14 = 7.714

9,290 - 7,714 = 1,576

1,576 / 8 = 197

551 - 197 = 354

197 x 22 + 354 x 14 = X

4.334 + 4.956 = X

Therefore, 197 adult tickets and 354 child tickets were sold for the event.