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 costs of the two plans are equal, we can set up an equation based on the given costs.

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

1. The cost for the first option (paying $10 per visit) is:
\[
10x
\]

2. The cost for the second option (paying $32 per month plus $6 per visit) is:
\[
32 + 6x
\]

We want to find the point where these two costs are equal:
\[
10x = 32 + 6x
\]

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 number of visits at which the costs of the two plans are equal is \( x = 8 \).

The correct response is:
\[
10x = 32 + 6x; \quad x = 8
\]