An ice-skating ring 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 visit six dollars per per visit right in an equation share the numbers of visits it would take for the cost of the two plans to be equal.

Question

An ice-skating ring 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 visit six dollars per per visit right in an equation share the numbers of visits it would take for the cost of the two plans to be equal.

Answer 1

Let's denote the number of visits as x.

For the first option, the cost per visit is $10, so the cost for x visits is 10x.
For the second option, the cost per visit is $6, so the cost for x visits is 6x.
To find the number of visits for which the cost of the two plans is equal, we need to solve the equation:
10x = 32 + 6x
Subtracting 6x from both sides:
4x = 32
Dividing both sides by 4:
x = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.

Answer 2

To find the number of visits needed for the cost of the two plans to be equal, we can set up an equation.

Let's represent the number of visits as "x".

For the first option, the cost is $10 per visit, so the total cost would be 10x.

For the second option, the cost is $32 per visit plus an additional $6 per visit. Therefore, the total cost would be (32 + 6)x, which simplifies to 38x.

We can now set up the equation:

10x = 38x

To solve for x, we can subtract 10x from both sides of the equation:

10x - 10x = 38x - 10x

0 = 28x

Dividing both sides by 28, we get:

0/28 = 28x/28

0 = x

Therefore, the cost of the two plans will never be equal, as there are no positive values for x that make the equation true.

Answer 3

To find the number of visits it would take for the cost of the two plans to be equal, we can set up an equation.

Let's assume that x represents the number of visits.

For the first option, we pay $10 per visit. So the cost would be 10x.

For the second option, we have to pay $32 per visit plus an additional $6 per visit. So the cost would be 32x + 6x.

To find when the costs are equal, we can set up the equation:

10x = 32x + 6x

Combining like terms, we get:

10x = 38x

Now, we can subtract 38x from both sides to isolate x:

10x - 38x = 38x - 38x

-28x = 0

Finally, divide both sides by -28 to solve for x:

x = 0

Therefore, the cost of the two plans will be equal when the number of visits is 0.

However, it's important to note that in this case, 0 visits means not using the facility at all. In practical terms, it's impossible for 0 visits to have equal costs.