A10 foot board is to be cut into two pieces, so that the longer piece is 4 times the length of the shorter piece. find the length of each piece

So, we know the longer piece is 4 times the shorter

Then we are told these two pieces were cut from a 10 ft board so we can write an equation to solve for the shorter piece

short piece + long piece = 10 ft

(x means short piece)

x + 4x = 10

5x = 10    

x = 2

(Now use this to find the long piece )

(long piece is 4x )

4*2=8

So your answer is: short piece is 2 ft  and long piece is 8 ft

2 + 8 = 10