Question

A dance studio has two participation plans. For the first plan, the cost is $20 per visit. For the second plan, the cost is $45 per month, and $5 per visit. Write an equation to show the number of visits per month that it would take for the two plans to be equal. Use x
as your variable. (1 point)
Responses

45x=20+5x
45 x equals 20 plus 5 x

20x=45x+5
20 x equals 45 x plus 5

20x=45+5x
20 x equals 45 plus 5 x

5x=20x+45

Answer 1

To find the number of visits per month at which the cost of the two plans is equal, we need to set up equations for both plans.

1. **First Plan**: The cost is $20 per visit. If we let \( x \) be the number of visits, the total cost for this plan is:
\[
\text{Cost for Plan 1} = 20x
\]

2. **Second Plan**: The cost is $45 per month plus $5 per visit. Therefore, the total cost for this plan is:
\[
\text{Cost for Plan 2} = 45 + 5x
\]

We want to find \( x \) such that both costs are equal:
\[
20x = 45 + 5x
\]

This equation matches with the first option provided in your responses:
**45x = 20 + 5x**

So the correct equation representing the situation is:
\[
20x = 45 + 5x
\]

This shows the number of visits per month at which the costs of the two plans are equal.