GRE Statistics Problem Matt gets \$1000 commission on a big sale.This commission alone raises his average commission by \$150. if Matt's new average commission is $400, how many sales has Matt made?
I feel this question is missing some information but the book has a solution. Am i missing something?
 A: Hint: Let $n$ be the number of sales Matt has made, $T$ the total commission Matt has earned, including the most recent sale. How would you calculate his current average commission (if you didn't know it already) from these values? How would you calculate the average commission prior to his most recent sale? From these calculations, you will have two linear equations in the two variables $n$ and $T$, from which you should be able to determine $n$ (and $T$, of course).
A: You can even do it by trial and error. Since his average commission is raised 150 dollars. Then we know his original average was 250.By trial and error I multiplied 250*4=1000 Add another 1000 dollars and we get  2000. And 2000/5 is 400 average. Thus he has made 5 sales.
A: long time has passed since the question was asked but i'll explain it for newest guests.
So, if we take "n" as the # of sales (n=# of sales) and "T" for total comissions; then our first equaiton is; 250n=T,
then, for instance, Matt gets a big sale and his total comissions rise to T+1000 and number of sales rise to "n+1" and new average commission becomes 400$. Therefore we have two equations.
250n=T
400(n+1)=1000+T
on first equation, if we multiply each side by minus "-", equation won't change. then;
-250n=-T
400n+400=1000+T  our new equations. Then we could sum each side of equations. 
So,
150n=600, then n=4
our final amount of sales is (n+1), then the number of sales that Matt has made is n+1 = 4+1 = 5
answer is 5
