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

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

10x=32+6x ; x=4

Answer 1

To find the number of visits at which the two payment options cost the same, we can set up the equation based on the given information.

1. **First option (pay per visit)**:
- Cost = $10 per visit. So for \( x \) visits, the cost is \( 10x \).

2. **Second option (monthly fee + pay per visit)**:
- Cost = $32 per month plus $6 per visit. So for \( x \) visits, the cost is \( 32 + 6x \).

We want to find the number of visits \( x \) such that the costs are equal:
\[
10x = 32 + 6x
\]

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

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

Step 2: Simplify:
\[
4x = 32
\]

Step 3: Divide both sides by 4:
\[
x = \frac{32}{4} = 8
\]

So the correct equation and solution is:
**10x = 32 + 6x ; x = 8**

Thus, the cost of the two plans will be equal after 8 visits.