Question

A yoga studio offered a special for high school students where new students could join for half off of the monthly fee (includes 6 classes), plus a one time processing fee of $8.25. Ten students took advantage of this special and the yoga studio collected $392.50. Which equation can be used to find r, the regular price of the monthly fee?

Answer 1

Given:

• the discounted price was offered by the yoga studio at 50% off the regular price 'r' (monthly fee).
• the one-time processing fee is $8.25
• 10 students took this offer and the yoga studio collected $392.50

To Find:

The regular price of the monthly fee 'r'

Solution:

The equation can be framed as

$(r-\frac{50}{100}.r)+8.25=39.25\\\frac{50}{100}.r+8.25=39.25\\\frac{r}{2}+8.25=39.25\\\frac{r}{2}=31\\r=(31)(2)=62$

And, the regular price of the monthly fee is $62.

Calculation:

We know that 10 students took the offer and the yoga studio collected $392.50. This means, using the Unitary Method, the studio has collected $(392.50/10) = $39.25 per student.

Now, if r denotes the regular price of the monthly fee, the offer runs a 50% discount on r.

So, the discounted price should be $(r - 50% of r) i.e., $r-\frac{50}{100}.r$

We must add to this the one time processing fee of $8.25

Therefore, the total price paid by one student would be

$(r-\frac{50}{100}.r)+8.25$

This must be equal to $39.25 as we have calculated this to be the amount collected by the yoga studio per person.

So, the equation can be framed as

$(r-\frac{50}{100}.r)+8.25=39.25\\\frac{50}{100}.r+8.25=39.25\\\frac{r}{2}+8.25=39.25\\\frac{r}{2}=31\\r=(31)(2)=62$

Thus, the regular price of the monthly fee is $62.