One number is 6 more than the other, if three times the sum of the two numbers is equal to 22 more than the larger number, what are the two numbers?

Let

Also, three times the sum of the two number (i.e. ) is equal to 22 more than the larger number (i.e. ). Note that is the largest, because it is 6 more than .

So, if we set the two expressions to be equal, and we substitute , we have

And since is 6 more than , we have