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