Percentage calucation help requested!

[Wordnerd]

Percentage calculation help requested!

Hi I need to know the percentage taken off of an item regulary priced at $174 and marked down to $34. Thank you.

 

[HallsofIvy]

Marked down from $174 to $34? Wow, now that's a mark down! There are two equivalent ways to do this:
The amount of mark down is $174- 134= $140. That is a fraction of \(\displaystyle \frac{140}{174}= 0.8045(approximately) which is 80.5%.

Or: $34 is 34/174= .195= 19.5%. Since the whole amount is 100%, 100- 19.5= 80.5%.\)

 

[JeffM]

Hi I need to know the percentage taken off of an item regulary priced at $174 and marked down to $34. Thank you.

The answer is

\(\displaystyle 100 * \dfrac{174 - 34}{174} \approx 80.46\%.\)

To let you do such problems on your own, here are the formulas and their derivation:

\(\displaystyle Let\ r = regular\ price.\)

\(\displaystyle Let\ d = percentage\ discount.\)

\(\displaystyle Let\ m = marked\)-\(\displaystyle down\ price.\)

\(\displaystyle m = r - \left(r * \dfrac{d}{100}\right) = r\left(1 - \dfrac{d}{100}\right) = r * \dfrac{100 - d}{100} \implies\)

\(\displaystyle r = \dfrac{100m}{100 - d} \implies\)

\(\displaystyle d = 100 * \dfrac{r - m}{r}\)

 

[Wordnerd]

Thank you

Thank you both for taking the time to respond and for showing the work! I'm a word freak,numbers... not so much. Great savings indeed!