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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=4 10 x equals 32 plus 6 x ; x equals 4 10x=32−6x ; x=2

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To find the number of visits (let's call it \( x \)) at which the costs of the two plans are equal, we need to set up the equations for both options.

  1. The first option (paying per visit) costs: \[ \text{Cost}_1 = 10x \] where \( x \) is the number of visits.

  2. The second option (paying a monthly fee plus per visit) costs: \[ \text{Cost}_2 = 32 + 6x \]

We want to find \( x \) when the costs are equal, so we set the two equations equal to each other: \[ 10x = 32 + 6x \]

Now, we can solve for \( x \). First, subtract \( 6x \) from both sides: \[ 10x - 6x = 32 \] \[ 4x = 32 \]

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

Thus, the number of visits at which the costs of the two plans are equal is \( x = 8 \).

The correct response is:

  • 10x = 32 + 6x; x = 8