Finding the average when two infos on averages are given

Question

This is one competitive exam's question. Can someone give me an easy explanation on how to solve this problem?

Question

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

I tries to use the avg formula,

Sum of N numbers = avg X Number of Terms

But I am not quite getting it

Answer 1

Let $n$ be the number of sales he has now made. Before the last sale he had made $n-1$ sales with an average commission of $800$ dollars, so his total commission was $800(n-1)$ dollars. He has now made $n$ sales at an average of $900$ dollars, total $900n$ dollars. Since the difference is his latest $2000$ dollar commission, $$900n=800(n-1)+2000\ .$$ See if you can solve this.