'Average' problem

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'Average' problem

by Elena89 » Mon Nov 14, 2011 2:13 am
Sam earned a $2,000 commission on a big sale, raising his average commission by $100. If Sam's new average commission is $900, how many sales has he made?

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by neelgandham » Mon Nov 14, 2011 2:49 am
Sam earned a $2,000 commission on a big sale, raising his average commission by $100. If Sam's new average commission is $900, how many sales has he made?

Let total number of sales prior to the big sale be S and
the average commission prior to the big sale be A
Total commission earned prior to the big sale = A*S
Total commission earned after the big sale = A*S + 2000
Total number of sales including the big sale = S+1

Question can be rephrased to What is the value of S+1 ?

900 = Average commission prior to the big sale + 100 = A+100
Implies A = 800

Average commission after the big sale be A = Total commission earned after the big sale/Total number of sales including the big sale
=> (A*S + 2000) / (S+1) = 900
=> (800S + 2000)/(S+1) = 900
=> 800S + 2000 = 900S + 900
=> 100S = 1100
=> S = 11

S+1 = 12 = Total number of sales he made !

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by shankar.ashwin » Mon Nov 14, 2011 3:48 am
You could also do this using allegations.

New commission = Old + 100 = 900.

Old = 800. Resultant = 900 and Addition is 2000. ( 8 and 20 mixed to give 9)

So, (20-9) / (9-8) = 11/1. ( 11 of 8 and 1 of 20)

So, 11 + 1= 12 commissions.

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Re: 'Average' problem

by [email protected] » Tue Sep 08, 2020 9:24 am
Elena89 wrote:
Mon Nov 14, 2011 2:13 am
Sam earned a $2,000 commission on a big sale, raising his average commission by $100. If Sam's new average commission is $900, how many sales has he made?
Solution:

Since his new average commission is $900, his old average commission must be $800. We can create the equation where n is the number of sales Sam has made before the big sale.

(800n + 2000) / (n + 1) = 900

800n + 2000 = 900n + 900

1100 = 100n

11 = n

Including the big sale, Sam has made 12 sales.

Answer: 12

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