The larger of two numbers is 10 more than three times the smaller number is larger number decreased by the smaller number is 80 what are the two numbers

One of my old math teachers taught me how to do this, and I'm going to project his words to you. Make two equations, one labeled smaller number, the other labeled larger number, and whatever number has the most detail, the other one is put as X.
Smaller number = x
Larger number = 3x+10
When you have those two equations down, you have another data section that tells you the value of the two numbers. In your case:
Larger number - Smaller number = 80.
Plugging in what we have:
(3x+10)-x=80
3x+10-x=80
2x+10=80
2x=70
2x/2=70/2
x=35...
Plugging back in for the larger number, since we found the smaller one:
3(35)+10=105+10=115
Your numbers are 115 and 35
Hope this helps.