The grasshopper, the frog and the mouse had a jumping contest. The grasshopper jumped w inches. The grasshopper jumped x inches farther than the frog and the mouse jumped y inches lesser than the frog. How much farther did the grasshopper jump than the mouse?
The frog jumped f inches.

The grasshopper jumped w inches.

The mouse jumped m inches.

The frog jumped f inches.

The grasshopper jumped w inches.

The mouse jumped m inches.

The grasshopper jumped x inches farther than the frog.

The mouse jumped y inches lesser than the frog.

Now we have a system of 3 equations with 3 unknowns:

f + x = w

f - y = m

x - y = z

where z is the number of inches the grasshopper jumped farther than the mouse.

We can solve this system using substitution:

f + x = w

f - y = m

x - y = z

f = w - x

m = f + y

z = x - y

w - x + x - y = z

w - x = z

w - (w - x) = z

x = z