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.

Question

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)

• 10х = 32 + 6x; x = 8

• 10 = 32 + 6x ; x =-3

• 10х = 32 + 6x; x = 4

О 10х = 32 - 6x ; x = 2

Answer 1

To find the point where the costs of the two options are equal, we can set up an equation based on the information provided.

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

1. The cost for the first option (paying $10 per visit) is: \[ 10x \]

2. The cost for the second option (paying $32 per month and $6 per visit) is: \[ 32 + 6x \]

To find the number of visits where the costs are equal, we set the two expressions equal to each other: \[ 10x = 32 + 6x \]

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

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

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

So, the solution to the equation is \( x = 8 \). This means that after 8 visits, the costs of both plans will be equal.

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