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=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

10x=32+6x
; x=8
10 x equals 32 plus 6 x ; x equals 8

10=32+6x
; x=−3

Answer 1

To find the number of visits \( x \) for which the costs of the two plans would be equal, we need to set up the equations for both options.

1. The first option (paying per visit):

   • Cost = \( 10x \)

2. The second option (paying a monthly fee and then per visit):

   • Cost = \( 32 + 6x \)

Now, we set these two expressions equal to each other to find the number of visits where the costs are the same:

\[ 10x = 32 + 6x \]

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

1. Subtract \( 6x \) from both sides: \[ 10x - 6x = 32 \] \[ 4x = 32 \]

2. Divide both sides by 4: \[ x = 8 \]

So, the correct equation is \( 10x = 32 + 6x \) and the solution is \( x = 8 \).

This means it would take 8 visits for the cost of the two plans to be equal. Therefore, the correct response is:

10x = 32 + 6x ; x = 8.