The sum of 2 numbers is 22. three times one number is equal to ten more than the other. find the numbers

Translating that problem into an equation with x as a variable we get 3x + x +10 = 22. Combine like terms to get 4x + 10 = 22. Subtract 10 on both sides to get 4x = 12. Divide by 4 on both sides to get x = 3. 

Now to plug in. The first number was represented by 3x. So substituting 3 for the x we get 3(3) = 9. And again for the second number represented by x+10, 3+10 = 13. 

Your numbers are 9 and 13. To check just add them together. 13 + 9 is 22, I'll save ya the effort.