Question

JC has a VIP membership to a movie theater, so she pays $27 a year and six dollars for each movie she sees. Claire doesn't have a membership, so she pays $8.25 each movie she sees. How many movies would they have to see in a year in order to pay the same amount that year.

Answer 1

12 movies

Explanation:

Given

VIP

`Base\ Amount = \$27`

`Per\ movie = \$6`

Regular

`Per\ movie = \$8.25`

Required

Determine the number of movies where they pay the same amount

Represent the number of movies with m.

For VIP, we have..

`Expression = 27 + 6 * m`

`Expression = 27 + 6m`

For regular, we have

`Expression = 8.25 * m`

`Expression = 8.25m`

Equate both expressions

`8.25m = 27 + 6m`

Collect Like Terms

`8.25m - 6m = 27`

`2.25m = 27`

Solve for m

`m = 27/2.25`

`m = 12`