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

Question

Isaiah Anthony · Accepted Answer

#5# movies

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 + 7M# club 2: #" "C_2 = 12M# For the clubs cost to be equal: #C_1 = C_2# #25 + 7M = 12M# Subtract #7M# 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#

Kennedy Adams · Answer

undefined Let $ x $ represent the number of movies purchased. The total cost for the first club is $ 25 + 7x $, and for the second club, it's $ 12x $. To find when they are equal, solve the equation $ 25 + 7x = 12x $ for $ x $. $ x = 5 $. So, a member must purchase 5 movies for the cost of the two clubs to be equal.

Hazel Anglin · Answer

undefined Let $x$ represent the number of movies purchased.

For the first club (with a one-time fee of $25 and $7 per movie), the total cost is $25 + 7x$.

For the second club (with no one-time fee and $12 per movie), the total cost is $12x$.

To find when the costs are equal, set the two expressions equal to each other and solve for $x$:

$$25 + 7x = 12x$$

$$25 = 12x - 7x$$

$$25 = 5x$$

$$x = \frac{25}{5}$$

$$x = 5$$

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