Matt needs help!

rrobiinn wrote:Matt gets a $1,000 commission on a big sale.This commission alone raises his aver-age commission by $150.If Matt's new average commission is $400,how many sales has Matt made?

- I found the solution like this:

"s=total number of things sold (before big sale) It should be total commission on the previous sales.
x=number of things sold (before big sale)

so s/x = 250
s = 250x

after big sale

(s+1000)/(x+1) = 400

s+1000 = 400x+400

since s = 250x

250x+1000 = 400x+400

150x = 600

x= 4

so after the big commision, sales are x+1 = 4+1 = 5"

I don't understand why it is (x+1), meaning the sales has increased by 1, after the big sale. how come (x+1) !

a big sale = 1 sale
x = # of sales before the big sale
=> total # of sales after the big sale = x+1

rrobiinn wrote:Matt gets a $1,000 commission on a big sale.This commission alone raises his aver-age commission by $150.If Matt's new average commission is $400,how many sales has Matt made?

Old sum before the sale = (old number of sales)(old average) = x(250) = 250x.
New sum after the big sale = (new number of sales)(new average) = (x+1)400 = 400x + 400.
Since the new sum is 1000 greater than the old sum:
400x + 400 = 250x + 1000
150x = 600
x = 4.
New number of sales = x+1 = 4+1 = 5.

When taking the GMAT, we could plug in the answer choices, which would represent the number of sales AFTER the big sale.
When the correct answer is plugged in, the difference between the new sum (at an average of 400 per sale) and the old sum (at an average of 250 per sale) must be 1000.
Given the following answer choices:

2
3
4
5
6

Answer choice C: 4
New sum - old sum = 4(400) - 3(250) = 850.
Too small.
Eliminate A, B and C.

Answer choice D: 5
New sum - old sum = 5(400) - 4(250) = 1000.
Success!

The correct answer is D.