Alfredo enjoys going to a local trampoline center. He can pay in one of two ways: Plan A requires him to pay $48 for a year's membership, but during that time he pays just $6 each time he visits the center. Plan B does not require a membership; however, under this plan Alfredo must pay $10 for each visit. Alfredo understands that if he visits the trampoline center infrequently, plan B is a better deal, but if he attends more often, plan A will ultimately cost less money. Alfredo wants to know how many times he must visit the center so that the total cost under both plan A and plan B will be equal. Write a linear equation to help him solve the problem. Then determine how many times Alfredo must visit the center for the two values to be the same. (4 points)

1 answer

Let x represent the number of times Alfredo visits the trampoline center.

Under Plan A:
Total cost = $48 (membership fee) + $6x (cost per visit)

Under Plan B:
Total cost = $10x (cost per visit)

Setting the total costs equal to each other:

$48 + $6x = $10x

Simplifying:

$48 = $4x

x = 12

Therefore, Alfredo must visit the trampoline center 12 times for the total cost under both plan A and plan B to be equal.