Question #7abdc

1 Answer
Feb 2, 2017

Answer:

#$34#

Explanation:

In order to find the amount of money Albert had on his paycheck, you must express this value in terms of the amount of money Richard has on his paycheck.

The problem tells you that Richard had

...twice the difference of Albert's paycheck dollars and #9#

Let's break this information down to see if we can find a relationship between the value of the two paychecks.

For starters,

...twice the difference...

means that you must double the value of a difference, i.e. multiply the difference by #color(blue)(2)#. What difference is the problem referring to?

the difference of Albert's paycheck dollars and #9# [presumably dollars]

So if we take #A# to represent the value of Albert's paycheck, we can say that the difference between #A# and #$9# will be

#A - $9 " "-># we've subtracted #$9# from the value fo Albert's paycheck

We now have to double this difference in order to find the value of Richard's paycheck, let's say #R#

#color(red)(ul(color(black)(R = color(blue)(2) * (A - $9))))#

And that is the equation that we're looking for. We now have a way of expressing the value of Albert's paycheck in terms of the value of Richard's paycheck.

Rearrange the equation to solve for #A#. Divide both sides by #2#

#R/2 = color(red)(cancel(color(black)(2)))/color(red)(cancel(color(black)(2))) xx (A - 9)#

#R/2 = A - 9#

Add #9# to both sides to get

#R/2 + 9 = A - color(red)(cancel(color(black)(9))) + color(red)(cancel(color(black)(9)))#

This is equivalent to

#A = R/2 + $9#

We know that Richard had #$50# on his paycheck, so plug that value in for #R# to find the value of Albert's paycheck

#A = ($50)/2 + $9#

#color(darkgreen)(ul(color(black)(A = $25 + $9 = $34)))#

Therefore, you can say that Albert had #$34# on his paycheck.