Question

A gym offers two payment plans. Plan A: $110 annual fee plus $1 per visit. Plan B: $10 annual fee plus $5 per visit. Write and solve (showing each step) an equation to determine the number of visits (v) that would make both plans cost the same.

Answer 1

110 + v = 10 + 5v

10 + 4v = 110

4v = 100

v = 25 visits

Answer 2

To find the number of visits at which both gym payment plans cost the same, we set up the equation 110 + 1v = 10 + 5v and solve for v. After simplifying, we find that at 25 visits, both Plan A and Plan B would cost the same.

Step-by-step explanation:

To determine the number of visits (v) that would make the cost of both Plan A and Plan B the same, we need to set up an equation where the total cost of each plan is equal. Plan A has a $110 annual fee plus $1 per visit, so its total cost can be represented as 110 + 1v. Plan B has a $10 annual fee plus $5 per visit, so its total cost is 10 + 5v.

Setting these equations equal to each other, we have:

• 110 + 1v = 10 + 5v

To solve for v, we follow these steps:

1. Subtract 1v from both sides to get the variable on one side: 110 = 10 + 4v
2. Subtract 10 from both sides to isolate the term with v: 100 = 4v
3. Divide both sides by 4 to solve for v: 25 = v

Therefore, after 25 visits, both plans would cost the same.