I'm having trouble with setting up problems that deal with two average formulas (An example would be the problem listed on Pg. 104 of Guide #4 [Word Translations]).

Problem: Sam earned a $2000 commission on a big sale, raising his avg. commission by $100. If Sam's new avg. commission is $900, how many sales has he made?

Even though the solution is listed in the guide, I can't quite grasp the concept correctly and consistently applying the steps on the In-Action problems (Namely, #8 & 10). Is there a video that teaches these types of questions specifically either by Ron or other instructors?

I tried searching for "Thursdays with Ron" videos by looking for ones that discussed about averages. But, they all deal with the topic of weighted averages, and I believe these problems are not considered as weighted averages since they're listed on a different section within the chapter.

If anyone can point me to the right video or tell me the name of these types of questions, it would be helpful.

Thank you!

i don't know of any relevant videos, but the main thing to consider with problems that have two different averages is that you should often look for the total. this one is a little tricky in terms of the totals because you have to introduce variables, but the concept is the same..

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Tim Sanders
Manhattan GMAT Instructor

I believe the solution would be something like this

Consider his average s X
then, since his new average is 900 after increasing by 100, we an write the equation

X+100=900

Also, he recieved y commissions before getting the 2000 commission

then, (Xy+2000)/y+1= 900
which when translated means

800y+2000=900y+900
1100/100=y
y=11

Would be great if you could confirm this.

krishnan, correct! Let's break it down a bit more and define some variables.

I figured that if the new average is $900, $100 more than the old average (as the problem states), then the old average is $800.

Average = Total/Number of things. Thus the old average of $800= total old revenue/number of sales. Let's call old number of sales "n". Thus, $800 = total old revenue/n. Multiply by n on both sides, and total old revenue is $800n.

New average revenue is $900. Thus, $900 = new total revenue/new number of sales. New total revenue is old revenue (800n) + new sale (2000). New number of sales is n (old number of sales) + 1 (new sale). Let's put this together:

900= (800n + 2000)/(n+1). Multiply n+1 across and you get:
900(n+1)=800n + 2000
thus
900n + 900 = 800n + 2000
100n=1100
n=11
Thus, our old number of sales is 11. Given that he just made the one new $2000 sale, total number of sales is 12.

I hope that this helps! :-)

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Jamie Nelson
ManhattanGMAT Instructor