Question

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)

Answer 1

To find out how many times Alfredo must visit the trampoline center for the total costs under Plan A and Plan B to be equal, we'll start by writing the cost equations for both plans.

1. **Cost for Plan A**: The total cost consists of the membership fee plus the cost per visit:
\[
\text{Cost}_A = 48 + 6x
\]
where \( x \) is the number of visits Alfredo makes.

2. **Cost for Plan B**: The total cost for this plan is simply the cost per visit multiplied by the number of visits:
\[
\text{Cost}_B = 10x
\]

To find the number of visits where both costs are equal, we set the two equations equal to each other:
\[
48 + 6x = 10x
\]

Next, we'll solve for \( x \):

1. Subtract \( 6x \) from both sides:
\[
48 = 10x - 6x
\]
\[
48 = 4x
\]

2. Now, divide both sides by 4:
\[
x = \frac{48}{4}
\]
\[
x = 12
\]

Thus, Alfredo must visit the trampoline center **12 times** for the total costs under both plans to be equal.