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](https://tex.z-dn.net/?f=%28r-%5Cfrac%7B50%7D%7B100%7D.r%29%2B8.25%3D39.25%5C%5C%5Cfrac%7B50%7D%7B100%7D.r%2B8.25%3D39.25%5C%5C%5Cfrac%7Br%7D%7B2%7D%2B8.25%3D39.25%5C%5C%5Cfrac%7Br%7D%7B2%7D%3D31%5C%5Cr%3D%2831%29%282%29%3D62)
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](https://tex.z-dn.net/?f=r-%5Cfrac%7B50%7D%7B100%7D.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](https://tex.z-dn.net/?f=%28r-%5Cfrac%7B50%7D%7B100%7D.r%29%2B8.25)
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](https://tex.z-dn.net/?f=%28r-%5Cfrac%7B50%7D%7B100%7D.r%29%2B8.25%3D39.25%5C%5C%5Cfrac%7B50%7D%7B100%7D.r%2B8.25%3D39.25%5C%5C%5Cfrac%7Br%7D%7B2%7D%2B8.25%3D39.25%5C%5C%5Cfrac%7Br%7D%7B2%7D%3D31%5C%5Cr%3D%2831%29%282%29%3D62)
Thus, the regular price of the monthly fee is $62.