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=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=4

Answer 1

To find the number of visits at which the costs of the two plans are equal, we can set up the equation based on the given options.

1. The first option charges $10 per visit: \[ \text{Cost}_1 = 10x \]

2. The second option charges $32 per month and $6 per visit: \[ \text{Cost}_2 = 32 + 6x \]

Now we can set the two costs equal to each other to find the number of visits \( x \):

\[ 10x = 32 + 6x \]

Next, we will isolate \( x \) by moving \( 6x \) to the left side of the equation:

\[ 10x - 6x = 32 \] \[ 4x = 32 \]

Now, divide both sides by 4:

\[ x = \frac{32}{4} \] \[ x = 8 \]

Thus, the number of visits it takes for the cost of the two plans to be equal is 8.

So, the correct response is: 10x = 32 + 6x ; x = 8.