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 = $\displaystyle x$

John = Monica earns three times per hour as John, therefore John earns 1/3 in comparison to Monica $\displaystyle = \frac{1}{3x}$

Alicia = receives $2 less than John = $\displaystyle = \frac{1}{3x}-2$

The equation then becomes

$\displaystyle x + (\frac{1}{3x})+ (\frac{1}{3x} -2) = 43$

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 $\displaystyle x = 7$, did I make an error along the way or is all of the work completely wrong?

Thanks for your help

Re: Word Problem: Computing age comparing quantities

Quote:

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?

Make it easy on yourself. Start with John.

$\displaystyle m+j+a=3j+j+j-2=43$

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.

Re: Word Problem: Computing age comparing quantities

Quote:

Originally Posted by

**allyourbass2212** . But I would still like to know why I am not having success comparing quantities using Monica.

This $\displaystyle x + (\frac{1}{3x})+ (\frac{1}{3x} -2) = 43$ wrong.

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

Re: Word Problem: Computing age comparing quantities

Quote:

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, $\displaystyle x$

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

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

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

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

$\displaystyle 3x + x + x = 135$

$\displaystyle 5x = 135$

$\displaystyle x = 27$, monica

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

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