At the movie theatre, child admission is $6.00 and adult admission is $9.10. On Wednesday, four times as many adult tickets as child tickets were sold, for a total sales of $890.40.

Question

At the movie theatre, child admission is $6.00 and adult admission is $9.10. On Wednesday, four times as many adult tickets as child tickets were sold, for a total sales of $890.40. How many child tickets were sold that day?

Answer 1

We have 2 unknowns so we must find 2 equations to solve this problem.

Let x = number of adult tickets sold

y = number of child tickets sold

Eq. I: On Wednesday, the number of adult tickets sold was 4 times as many as child tickets, or x = 4y.

Eq. II: 9.10x + 6.00y = 890.40

Using the value for x from Eq. I in Eq. II we can solve y:

x = 4y Eq. I

9.10x + 6.00y = 890.40 Eq. II

9.10(4y) + 6.00y = 890.40 substitute for x

36.40y + 6.00y = 890.40 simplify

42.40y = 890.40

y = 890.40/42.40 divide both sides by 42.40 to isolate y

y = 21 solve for y

Use this value for y in Eq. I we can now solve for x:

x = 4y Eq. I

x = 4(21) substitute for y

x = 84 solve for x

The number of child tickets sold on that day is y = 21.