# Percents Word Problem Translation

• Apr 1st 2011, 06:02 AM
dumluck
Percents Word Problem Translation
Hi All,
Question: "x is what percent of y percent of z, in terms of x,y,z"

Y percent of z = $\frac{y}{100}.z$

X percent of y percent of z = $\frac{w}{100}.\frac{y}{100}.z$

This is where it gets confusing for me.

This translates to x = $\frac{w(\frac{yz}{100})}{100}$

Question one: I'm not sure how $\frac{w}{100}.\frac{y}{100}.z$ transforms into $\frac{w(\frac{yz}{100})}{100}$

Question two: I'm not sure how $\frac{w(\frac{yz}{100})}{100}$ transforms into $w = \frac{100x}{\frac{yz}{100}}$

Question three: I'm not sure how $w = \frac{100x}{\frac{yz}{100}}$transforms into $w = \frac{10,000x}{yz}$

There just seems to be jumps in logic that I'm not getting.

Thx,
D
• Apr 1st 2011, 07:17 AM
Quacky
Quote:

Question one: I'm not sure how $\frac{w}{100}.\frac{y}{100}.z$ transforms into $\frac{w(\frac{yz}{100})}{100}$
It is a very strange setup!

$\frac{w}{100}\times\frac{y}{100}\times~z$

$=\frac{w}{100}\times\frac{yz}{100}$

$=\dfrac{\frac{w\times~yz}{100}}{100}$

$=\frac{w\times\frac{yz}{100}}{100}$

Although why you'd set something out so poorly is beyond me!

Quote:

Question two: I'm not sure how $\frac{w(\frac{yz}{100})}{100}$ transforms into $w = \frac{100x}{\frac{yz}{100}}$
Again, this is a dreadful approach! I'd not even bother going whatever route they've taken. Starting at:

$x=\frac{w(\frac{yz}{100})}{100}$, multiply both sides by 100:

$100x=w\times\frac{yz}{100}$ Then do it again:

$10000x=w\times~yz$ Now divide both sides by $yz$
$
\frac{10000x}{yz}=w$

Do you follow my method? The approach you've been shown is really quite bad. (Speechless)
• Apr 1st 2011, 07:21 AM
earboth
Quote:

Originally Posted by dumluck
Hi All,
Question: "x is what percent of y percent of z, in terms of x,y,z"

Y percent of z = $\frac{y}{100}.z$

X percent of y percent of z = $\frac{w}{100}.\frac{y}{100}.z$

This is where it gets confusing for me.

This translates to x = $\frac{w(\frac{yz}{100})}{100}$

Question one: I'm not sure how $\frac{w}{100}.\frac{y}{100}.z$ transforms into $\frac{w(\frac{yz}{100})}{100}$

$\frac{w}{100} \cdot \frac{y}{100}\cdot z = \dfrac1{100} \cdot w \cdot \left( \dfrac{y z}{100} \right) = \dfrac1{100} \cdot \left( w \cdot \left( \dfrac{y z}{100} \right) \right) = \dfrac{\left( w \cdot \left( \dfrac{y z}{100} \right) \right)}{100}$

Quote:

Question two: I'm not sure how $\frac{w(\frac{yz}{100})}{100}$ transforms into $w = \frac{100x}{\frac{yz}{100}}$
$x=\dfrac{w(\frac{yz}{100})}{100}~\implies~100x=w(\ frac{yz}{100})~\implies~w=\dfrac{100x}{\frac{yz}{1 00}}$
Quote:

Question three: I'm not sure how $w = \frac{100x}{\frac{yz}{100}}$transforms into $w = \frac{10,000x}{yz}$

There just seems to be jumps in logic that I'm not getting.

Thx,
D
I'll leave the last step for you: You have to divide a term (100x) by a fraction. How do you do this usually?
• Apr 1st 2011, 07:52 AM
dumluck
Quote:

Originally Posted by earboth
$\frac{w}{100} \cdot \frac{y}{100}\cdot z = \dfrac1{100} \cdot w \cdot \left( \dfrac{y z}{100} \right) = \dfrac1{100} \cdot \left( w \cdot \left( \dfrac{y z}{100} \right) \right) = \dfrac{\left( w \cdot \left( \dfrac{y z}{100} \right) \right)}{100}$

$x=\dfrac{w(\frac{yz}{100})}{100}~\implies~100x=w(\ frac{yz}{100})~\implies~w=\dfrac{100x}{\frac{yz}{1 00}}$

I'll leave the last step for you: You have to divide a term (100x) by a fraction. How do you do this usually?

multiply the reciprical of the denoiminator. Thanks to you both.