Question

A movie club charges a one-time membership fee of $25. It allows members to purchase movies for $7 each. Another club does not charge a membership fee and sells movies for $12 each. How many movies must a member purchase for the total cost of the two clubs to be equal?

Answer 1

Answer: $$5$$ movies

Step-by-step explanation: Given: A movie club, one time fee

=

$

25

, movies

=

$

7

       

2nd club,

$

0

fee, movies

=

$

12

Cost equations for each club:

club 1:

C

1

=

25

+

7

M

club 2:

C

2

=

12

M

For the clubs cost to be equal:

C

1

=

C

2

25

+

7

M

=

12

M

Subtract

7

M

from both sides:

25

=

5

M

Divide by

5

:

M

=

25

5

=

5

5

movies

CHECK:

C

1

=

25

+

7

⋅

5

=

25

+

35

=

$

60

C

2

=

12

⋅

5

=

$

60

Answer 2

Answer:

5 movies

Step-by-step explanation:

Define the variables:

• x = number of movies purchased

• y = total cost

Create two equations from the given information.

Equation 1

Given:

• A movie club charges a one-time membership fee of $25.
• It allows members to purchase movies for $7 each.

⇒ y = 25 + 7x

Equation 2

Given:

• Another club does not charge a membership fee.
• It sells movies for $12 each.

⇒ y = 12x

To find how many movies a member must purchase for the total cost of the two clubs to be equal, substitute Equation 2 into Equation 1 and solve for x:

⇒ 12x = 25 + 7x

⇒ 12x - 7x = 25 + 7x - 7x

⇒ 5x = 25

⇒ 5x ÷ 5 = 25 ÷ 5

⇒ x = 5

Therefore, a member must purchase 5 movies for the total cost of the two clubs to be equal.

Learn more about systems of equations here:

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