Question

An ice skating rink has two ways you can use the facility. The first option is to pay $10 per visit. The second option is to pay $32 per month, and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal.(1 point)
Responses

10x=32+6x
; x=8
10 x equals 32 plus 6 x ; x equals 8

10x=32+6x
; x=4
10 x equals 32 plus 6 x ; x equals 4

10x=32−6x
; x=2
10 x equals 32 minus 6 x ; x equals 2

10=32+6x
; x=−3

Answer 1

To find the number of visits (x) where the costs of the two options are equal, we can set up the equation based on the information provided:

1. **First Option (Pay per visit)**: The cost is \(10x\) where \(x\) is the number of visits.
2. **Second Option (Monthly fee + Pay per visit)**: The cost is \(32 + 6x\).

To find the number of visits where both options cost the same:

\[
10x = 32 + 6x
\]

Now, let's solve for \(x\):

1. Subtract \(6x\) from both sides:

\[
10x - 6x = 32
\]
\[
4x = 32
\]

2. Now, divide both sides by 4:

\[
x = \frac{32}{4} = 8
\]

So, the correct response is:

**10x = 32 + 6x ; x = 8**

This means that after 8 visits, the costs of the two plans will be equal.