Question 257748
The difference between two numbers is 15. When twice the smaller number is subtracted from three times the larger number, the difference is 58. What is the larger number

Let x be the smaller and y the larger number.

Then:

1.) y - x = 15 and
2.) 3*y - 2*x = 58 

From 1.) we have y = x + 15. Substituting x + 15 for y in 2.) we have:

3*(x + 15) - 2*x = 58
3*x + 45 - 2*x = 58
x = 58 - 45
x = 13

Since y = x + 15:
y = 13 + 15
y = 28