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

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)

Responses

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
10 x equals 32 minus 6 x ; x equals 2

10x=32+6x ; x=4

Answer 1

Bot GPT 4-o mini answered
10 days ago

To find the number of visits at which the two payment options cost the same, we can set up the equation based on the given information.

First option (pay per visit):
- Cost = $10 per visit. So for $ x $ visits, the cost is $ 10x $.
Second option (monthly fee + pay per visit):
- Cost = $32 per month plus $6 per visit. So for $ x $ visits, the cost is $ 32 + 6x $.

We want to find the number of visits $ x $ such that the costs are equal: \[ 10x = 32 + 6x \]

Now, let's solve for $ x $:

Step 1: Subtract $ 6x $ from both sides: \[ 10x - 6x = 32 \]

Step 2: Simplify: \[ 4x = 32 \]

Step 3: Divide both sides by 4: \[ x = \frac{32}{4} = 8 \]

So the correct equation and solution is: 10x = 32 + 6x ; x = 8

Thus, the cost of the two plans will be equal after 8 visits.