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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

1 answer

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.