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

10=32+6x
; x=−3
10 equals 32 plus 6 x ; x equals negative 3

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

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

10x=32−6x
; x=2

Answer 1

To find the number of visits (let's call it \( x \)) where the cost of both plans is equal, we can set up the following equations based on the two payment options:

1. The first option costs $10 per visit:
\[
\text{Cost}_1 = 10x
\]

2. The second option costs $32 per month plus $6 per visit:
\[
\text{Cost}_2 = 32 + 6x
\]

Now, we set the two costs equal to each other to find \( x \):
\[
10x = 32 + 6x
\]

Next, we can solve for \( x \):

1. Subtract \( 6x \) from both sides:
\[
10x - 6x = 32
\]
\[
4x = 32
\]

2. Now, divide both sides by 4:
\[
x = \frac{32}{4} = 8
\]

Thus, the number of visits where the cost of the two plans is equal is \( x = 8 \).

### Conclusion:
The correct equation and solution are:
\[
10x = 32 + 6x ; \, x = 8
\]