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 two plans to be equal .

answers:

10x = 32 + 6x ; x = 4

10x = 32 + 6x ; = 8

10x = 32 + 6x ; 2

10x = 32 + 6x ; -3

Answer 1

you sure

Answer 2

To determine how many visits it would take for the costs of the two plans to be equal, we can set up an equation based on the information provided.

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

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

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

We want to find the value of \( x \) where both costs are equal:
\[
10x = 32 + 6x
\]

Now, let's solve for \( x \).

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

2. Simplifying the left side gives:
\[
4x = 32
\]

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

Thus, the number of visits it would take for the cost of the two plans to be equal is \( x = 8 \).

The correct answer is:
\[
10x = 32 + 6x ; x = 8
\]

Answer 3

Yes, I am sure. Let me clarify the steps taken to ensure understanding and correctness.

We set up the equation based on the provided cost models for the two options:

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

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

To find out when these two costs are equal, we set up the equation:
\[
10x = 32 + 6x
\]

Now, let's solve it step-by-step:

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

2. This simplifies to:
\[
4x = 32
\]

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

Therefore, it will take **8 visits** for the costs of the two plans to be equal.

So, the conclusion remains correct: **\( x = 8 \)**.