Question 743244
Let s = length of short piece of ribbon
Let L = length long piece of ribbon


"one piece is 24 inches longer than the other"
So L = s+24 [1]


"The longer piece is 4 times as long as the shorter piece."
So L = 4 s [2]


Sumstituting for L in [2] using [1]
L = s+24 = 4s


Subtracting s from both sides
24 = 3s
s=8 in.


Using [1] gives us L = s+24 = 8+24 = 32 in.

Checking in [2] L = 4 s = 4 x 8 = 32 QED.

The lengths are 8in and 32in.