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=4 10 x equals 32 plus 6 x ; x equals 4 10x=32−6x ; x=2

Answer 1

To find the number of visits (let's call it \( x \)) at which the costs of the two plans are equal, we need to set up the equations for both options.

1. The first option (paying per visit) costs:
\[
\text{Cost}_1 = 10x
\]
where \( x \) is the number of visits.

2. The second option (paying a monthly fee plus per visit) costs:
\[
\text{Cost}_2 = 32 + 6x
\]

We want to find \( x \) when the costs are equal, so we set the two equations equal to each other:
\[
10x = 32 + 6x
\]

Now, we can solve for \( x \). First, subtract \( 6x \) from both sides:
\[
10x - 6x = 32
\]
\[
4x = 32
\]

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

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

The correct response is:
- **10x = 32 + 6x; x = 8**