The sum of the three number is 92. the third is 3 times the first, the first number is 7 less than the second. what are the numbers?

Let x represent the first number, y represent the second, and z represent the third.

x + y + z = 92
z = 3x
x = y - 7

Solve x = y - 7 for y.
x = y - 7
x + 7 = y

Fill in y and z so that we only have to worry about x for now.

x + y + z = 92
x + (x + 7) + (3x) = 92
x + x + 7 + 3x = 92
5x + 7 = 92
5x = 92 - 7
5x = 85
x = 85/5
x = 17

Solve for y. 
y = x + 7
y = (17) + 7
y = 24

Solve for z.
z = 3x
z = 3(17)
z = 51

So x = 17, y = 24, and z = 51. 

Do the inverse operation