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)

Question

Responses

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
10 x equals 32 minus 6 x ; x equals 2

10=32+6x
; x=−3

Answer 1

To find the number of visits (x) where the costs of the two options are equal, we can set up the equation based on the information provided:

1. First Option (Pay per visit): The cost is \(10x\) where \(x\) is the number of visits.
2. Second Option (Monthly fee + Pay per visit): The cost is \(32 + 6x\).

To find the number of visits where both options cost the same:

\[ 10x = 32 + 6x \]

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 correct response is:

10x = 32 + 6x ; x = 8

This means that after 8 visits, the costs of the two plans will be equal.