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. 10x=32+6x ; x=8
2. 10x=32-6x ; x=2
3. 10x =32 +6x ; x=4
4.10=32+6x ; x=-3

Answer 1

To find the number of visits (\(x\)) at which the cost of both payment options is equal, we can set up the following equation:

1. The cost of the first option (pay-per-visit) is given by \(10x\), where \(x\) is the number of visits.
2. The cost of the second option (monthly fee plus per visit fee) is given by \(32 + 6x\).

Setting these two costs equal gives us the equation:
\[
10x = 32 + 6x
\]

Now, we can solve for \(x\):

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

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

Thus, it would take **8 visits** for the cost of the two plans to be equal.

Therefore, the correct answer is:
1. \(10x = 32 + 6x;\) \(x = 8\)