The larger of two numbers is seven less than three times the smaller number. if the sum of the numbers is 61, find the numbers.

So here is what we know:

Using what we know, our equation is .

Firstly, combine like terms:

Next, add 7 on both sides:

Next, divide both sides by 4 and the smaller number is

Now to find the larger number, plug 17 into the larger number expression to solve:

In short, the smaller number is 17 and the larger number is 44.