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 .

Question

answers:

10x = 32 + 6x ; x = 4

10x = 32 + 6x ; = 8

10x = 32 + 6x ; 2

10x = 32 + 6x ; -3

Answer 1

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 2

you sure

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: \( x = 8 \).