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

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=2

Answer 1

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

Option 1 costs: \[ 10x \quad \text{(pay $10 per visit)} \]

Option 2 costs: \[ 32 + 6x \quad \text{(pay $32 per month, plus $6 per visit)} \]

To find the number of visits where the costs are equal, set the two cost equations equal to each other: \[ 10x = 32 + 6x \]

Now, solve for \( x \):

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

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

So, the number of visits it would take for the cost of the two plans to be equal is \( \boxed{8} \).