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=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

10x=32+6x
; x=4
10 x equals 32 plus 6 x ; x equals 4

10=32+6x
; x=−3

Answer 1

To find the number of visits at which the cost of the two plans would be equal, let's denote:

• \( x \) as the number of visits.

Cost of the first option (paying $10 per visit): \[ \text{Cost}_1 = 10x \]

Cost of the second option (paying $32 per month, plus $6 per visit): \[ \text{Cost}_2 = 32 + 6x \]

Now, we can set these two expressions equal to find \( x \) when the costs are the same: \[ 10x = 32 + 6x \]

To solve for \( x \), we first isolate \( x \) by subtracting \( 6x \) from both sides: \[ 10x - 6x = 32 \] \[ 4x = 32 \]

Now, divide both sides by 4: \[ x = \frac{32}{4} \] \[ x = 8 \]

Thus, it takes 8 visits for the cost of the two plans to be equal. The correct response is:

• \( 10x = 32 + 6x; x = 8 \)