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) 10x = 32 + 6x; x = 4; 10x = 32 - 6x / x = 2; 10x = 32 + 6x / x = 8; 10 = 32 + 6xx = - 3

Answer 1

Let's start by defining the variable:

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

Now we can write the cost for each option:

1. For the first option (paying per visit): The cost is \( 10x \).
2. For the second option (monthly fee plus per visit fee): The cost is \( 32 + 6x \).

To find the number of visits where both costs are equal, we set the two equations equal to each other:

\[
10x = 32 + 6x
\]

Now, we will solve for \( x \):

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

\[
10x - 6x = 32
\]

\[
4x = 32
\]

2. 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 \( \boxed{8} \).