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
10 x equals 32 minus 6 x ; x equals 2

Answer 1

To determine the number of visits where the costs of the two options are equal, we can set up an equation based on the two pricing plans.

Let \( x \) be the number of visits.

1. The first option (pay-per-visit) costs \( 10x \) dollars.
2. The second option (monthly fee plus per-visit fee) costs \( 32 + 6x \) dollars.

To find the point where the costs are equal, we set up the equation:

\[
10x = 32 + 6x
\]

Now, let's solve the equation:

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

\[
10x - 6x = 32
\]

This simplifies to:

\[
4x = 32
\]

2. Divide both sides by 4:

\[
x = 8
\]

So, it would take 8 visits for the cost of the two plans to be equal.

The correct response comes from the option:
**10x = 32 + 6x ; x = 8.**