The larger of two numbers is 8 more than four times the smaller. If the larger is increased by four times the smaller, the result is 40. Find the numbers.

So let's make the smaller number x and the larger one y ...

Set up your equation by following the words signaling mathematical operations from the question.

y = 8 + 4x

y + 4x = 40

Now let's bring all variables to one side and solve the system if equations with elimination ...

y - 4x = 8

y + 4x = 40

Add the equations:

2y = 48

y = 24

Plug the y-value into one of the original equations:

24 = 8 + 4x

16 = 4x

4x = 16

x = 4

And there you have it! The smaller number [x] is 4 and the larger number [y] is 24.