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 where the costs of the two options are equal, we can set up an equation based on the cost structures of the two plans.

1. Plan 1 (Pay per visit):
   Cost = $10 per visit
   Total Cost for x visits = \(10x\)

2. Plan 2 (Monthly fee + Fee per visit):
   Cost = $32 per month + $6 per visit
   Total Cost for x visits = \(32 + 6x\)

Now, we set the two costs equal to each other:

\[ 10x = 32 + 6x \]

Next, we will solve this equation step-by-step:

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 \(x = 8\).

So the correct response is: \[ 10x = 32 + 6x ; x = 8 \] 10 x equals 32 plus 6 x ; x equals 8