# Thread: Word Problem: Computing age comparing quantities

1. ## Word Problem: Computing age comparing quantities

Problem: Monica earns three times per hour as John, John earns $2 more per hour than Alicia. Together they earn$43 per hour. How much is each one's hourly wage?

I attempted to compare each quantity in comparison to Monica

Monica = $x$
John = Monica earns three times per hour as John, therefore John earns 1/3 in comparison to Monica $= \frac{1}{3x}$
Alicia = receives $2 less than John = $= \frac{1}{3x}-2$ The equation then becomes $x + (\frac{1}{3x})+ (\frac{1}{3x} -2) = 43$ Clear out the fractions by multiplying every item by the LCD of 3, so on so forth but I do not get the correct answer. The correct answer is $x = 7$, did I make an error along the way or is all of the work completely wrong? Thanks for your help 2. ## Re: Word Problem: Computing age comparing quantities Originally Posted by allyourbass2212 Problem: Monica earns three times per hour as John, John earns$2 more per hour than Alicia. Together they earn \$43 per hour. How much is each one's hourly wage?
$m+j+a=3j+j+j-2=43$

3. ## Re: Word Problem: Computing age comparing quantities

Thanks Plato. Yes that is how I solved the problem after getting stuck on my initial approach. But I would still like to know why I am not having success comparing quantities using Monica.

4. ## Re: Word Problem: Computing age comparing quantities

Originally Posted by allyourbass2212
. But I would still like to know why I am not having success comparing quantities using Monica.
This $x + (\frac{1}{3x})+ (\frac{1}{3x} -2) = 43$ wrong.

It should be $x + (\frac{x}{3})+ (\frac{x}{3} -2) = 43$

5. ## Re: Word Problem: Computing age comparing quantities

Originally Posted by allyourbass2212
Thanks Plato. Yes that is how I solved the problem after getting stuck on my initial approach. But I would still like to know why I am not having success comparing quantities using Monica.
monica, $x$

john, $\frac{x}{3}$

alicia, $\frac{x}{3}-2$

$x + \frac{x}{3} + \frac{x}{3} - 2 = 43$

$x + \frac{x}{3} + \frac{x}{3} = 45$

$3x + x + x = 135$

$5x = 135$

$x = 27$, monica

$\frac{x}{3} = 9$, john

$\frac{x}{3} - 2 = 7$, alicia