# Thread: Percent Greater than Problem?

1. ## Percent Greater than Problem?

If q is 10% greater than p and r is 10% greater than y, qr is what percent greater than py?
I set up the following equations, Q=10/100(p)+p
R=10/100(y)+y
QR=x/100(py)+py
How do I solve them? I would appreciate any response.

2. ## Re: Percent Greater than Problem?

Hello, Sewilliams13!

$\displaystyle \text{If }q\text{ is 10\% greater than }p\text{, and }r\text{ is 10\% greater than }y,$
$\displaystyle qr\text{ is what percent greater than }py\,?$

I prefer simpler fractions.

$\displaystyle [1]\;q \:=\:p + \tfrac{1}{10}p \quad\Rightarrow\quad q \:=\:\tfrac{11}{10}p$

$\displaystyle [2]\;r \:=\:y + \tfrac{1}{10}y \quad\Rightarrow\quad r \:=\:\tfrac{11}{10}y$

Multiply [1] and [2]: .$\displaystyle qr \:=\:\left(\tfrac{11}{10}\right)^2py \;=\;\tfrac{121}{100}py \;=\;\left(1 + \tfrac{21}{100}\right)py$

. . . . . . . . . . . . . . . . $\displaystyle qr \;=\;py + \tfrac{21}{100}py$

$\displaystyle \text{Therefore, }qr\text{ is 21\% greater than }py.$

3. ## Re: Percent Greater than Problem?

In [1] & [2] why did you take a way the p and the y in the next equation

4. ## Re: Percent Greater than Problem?

They were not "taken away"; they were simply added together; like, 1 + 1/10 = 10/10 + 1/10 = 11/10

5. ## Re: Percent Greater than Problem?

-_-Ahh...Thank you so much!