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

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=4

Answer 1

To find the number of visits where the cost of the two plans is equal, we can set up an equation for the total cost.

Let \( x \) be the number of visits.

1. For the first option (paying $10 per visit), the total cost is: \[ \text{Cost}_1 = 10x \]

2. For the second option (paying $32 per month plus $6 per visit), the total cost is: \[ \text{Cost}_2 = 32 + 6x \]

We want to find \( x \) such that the costs are equal: \[ 10x = 32 + 6x \]

Now, let's solve the equation:

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 8 visits.

The correct equation and solution is: \[ 10x = 32 + 6x ; ; ; x = 8 \]