Video that deals setting up 2 avg. formulas...

[jackchang1029]

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!

[tim]

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..

[krishnan.anju1987]

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.

[jnelson0612]

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! :-)

[JbhB682]

Hi - Just wondering

Can this be done without algebra ? Perhaps using logic or teeter totter average method ?

Thank you !

[Sage Pearce-Higgins]

Absolutely it can. The new average ($900) is "weighted" between the old average ($800) and the $2000 commission for the single big sale. If you wrote this out in a line it would be 800---900-----------------------2000. The distance between the past sales and the average (100) is much shorter than the distance between the big sale and the average (1100), showing that there's much more "weight" on the 800, i.e. the number of sales is higher at that end of the scale. To use this to work out a precise number, compare the distances 100 and 1100. The ratio 'number of $2000 sales': 'number of $800 sales' is 100:1100, i.e. 1:11. So he's made 12 sales in total.