Question

For Saturday matinees, a movie theater charges $5 for adult tickets and $3 for children's tickets. If the movie theater sold a total of 166 matinee tickets and made

$718 in revenue on Saturday afternoon, how many adult matinee tickets were sold?

Answer 1

Explanation:

Let's use the following variables:

a = number of adult tickets sold

c = number of children tickets sold

We know that:

a + c = 166 (total number of tickets sold)

5a + 3c = 718 (total revenue)

We can solve this system of equations by substitution or elimination. Here, we'll use elimination:

Multiply the first equation by 3: 3a + 3c = 498

Subtract the second equation from the first: 2a = 220

Solve for a: a = 110

So 110 adult tickets were sold. We can find the number of children's tickets by substituting a = 110 into either of the original equations:

c = 166 - a = 166 - 110 = 56

Therefore, 110 adult tickets and 56 children's tickets were sold.

Answer 2

Let's use A to represent the number of adult tickets sold and C to represent the number of children's tickets sold.

We know that A + C = 166, since the total number of tickets sold is 166.

We also know that the revenue earned from adult tickets is $5A and the revenue earned from children's tickets is $3C. Since the total revenue earned is $718, we can write:

5A + 3C = 718

Now we have two equations with two variables:

A + C = 166

5A + 3C = 718

We can solve for A in the first equation to get:

A = 166 - C

Then we can substitute this expression for A into the second equation:

5(166 - C) + 3C = 718

Simplifying and solving for C, we get:

830 - 2C = 718

2C = 112

C = 56

So 56 children's tickets were sold. We can substitute this value back into the first equation to solve for A:

A + 56 = 166

A = 110

Therefore, 110 adult tickets were sold.