The sum of two numbers is 44. one number is 3 times as large as the other. what are the numbers?

Set up 2 variables:
x = larger number
y = smaller number

Set up equations:



Solve by substituting. I will use the x already given to us (in second equation) to substitute in 1st equation (x = 3y):




Plug it back into 2nd equation to solve for x:



So, our two values are: x = 33 and y = 11.

We can check, x + y = 33 + 11 does equal 44 and 33 times is 3 times larger than 11. So, the initial criteria work out and we are right.