A yoga studio has two participation plans. For the first plan, the cost is $8 per visit. For the second plan, the cost is $40 per month, and $2 per visit. Write an equation to show the number of visits per month that it would take for the two plans to be equal. Use x as your variable.

Question

[_] x = [_] + [_]

Answer 1

To find the number of visits per month at which the two plans would cost the same, we can set up the following equations based on the two plans:

1. For the first plan (cost per visit): \(8x\) (where \(x\) is the number of visits).
2. For the second plan (monthly fee plus cost per visit): \(40 + 2x\).

To find the number of visits where the costs are equal, we can set the two equations equal to each other:

\[ 8x = 40 + 2x \]

Now, we can rearrange this equation to solve for \(x\):

1. Subtract \(2x\) from both sides:

\[ 8x - 2x = 40 \]

2. This simplifies to:

\[ 6x = 40 \]

3. Now, divide both sides by 6:

\[ x = \frac{40}{6} \]

4. This simplifies to:

\[ x = \frac{20}{3} \quad \text{or} \quad x \approx 6.67 \]

Now, the original equation showing the number of visits (x) per month that makes the two plans equal can be expressed as:

\[ 8x = 40 + 2x \]

In the requested format for the equation:

\[ [] x = [] + [_] \]

You can fill in the blanks as follows:

\[ [8] x = [40] + [2] \]

So, the final equation is:

\[ 8x = 40 + 2 \]