Question

a 75 inch boars is cut into 2 pieces one piece is 4 times the length of the other find the lengths of the 2 pieces the short piece is _inches long

Answer 1

Length of the long piece = 4 times the length of the short piece
Length of the short piece = 1 times the length of the short piece.
Total length of both pieces = (4 + 1) = 5 times the length of the short piece.

5 times the length of the short piece = 75 inches

The length of the short piece =75 / 5 = 15 inches

Length of the long piece = 4 times the length of the short piece = 60 inches

Check: 15 + 60 = 75 inches
yay

Answer 2

The shorter piece is 15 inches, and the longer piece is 60 inches.
This would be a system of equations problem. If x is the shorter piece and y is the longer piece, then your two equations would be:
x + y = 75
y = 4x
Since the second equation tells you what y is, you can substitute the y in the first equation with 4x to get the equation x + 4x = 75. x + 4x is 5x, so you'll have 5x = 75. To get x by itself, divide off the 5 on both sides. 75 ÷ 5 = 15, so x = 15. The shorter piece would be 15 inches long.
Now that you know x, go to the second equation and plug it in: y = 4·15. 4·15 is 60, so that makes the longer piece 60 inches long.
Sorry if this was confusing; I'm really bad at giving written directions :/