Question

A theater seats 500 people. Each adult ticket, a, sells for $7.50, and each student ticket, s, for $4.50. On a Friday evening, every seat was filled, and the theater made $3,150 in ticket sales. Which system of equations could be used to find the number of adult and student tickets sold on Friday evening?

a + s = 3,150

7.5a + 4.5s = 3,150


a + s = 500

7.5a + 4.5s = 3,150


a + s = 3,150

7.5s + 4.5a = 500


a + s = 500

7.5a + 4.5s = 500

Answer 1

The two equations that can be used are 7.50a + 4.50s = 3150, and

a + s = 500.

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a + s = 3,150 NO

7.5a + 4.5s = 3,150 YES

a + s = 500 YES

7.5s + 4.5a = 500 NO

Explanation:

We know that a + s = 500.

Total sales would be the product of the number of adult and student tickets times their repsective prices:

Total Sales ($) = $7.50a + $4.50s = $3150

Leaving off the units for the next steps, we have two equations and we can rearrange one of them to substitute into the other.

1) Rearrange the first equation to isolate a: a = 500-s

Now use this definition of a in the second equation:

7.50a + 4.50s = 3150

7.50(500-s) + 4.50s = 3150

3750 - 7.5s + 4.50s = 3150

-3s = -600

s = 200 student tickets were sold

Use a+s=500 to find a:

a+200 = 500

a=300 300 adult tickets were sold.

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The two equations we used to find this answer were:

7.50a + 4.50s = 3150, and

a + s = 500