Question

A 20-inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces?

first piece ----
second piece----
Third piece----

Answer 1

First piece = one time
Second piece = 4 times
Third piece = 5 times

Total board before cutting: 10 times = 20 inches.

Divide each side by 10: 1 time = 2 inches

First piece (x) = 1 time = 2 inches
Second piece = 4 times = 8 inches
Third piece = 5 times=10 inches.

Check:
Total length of all 3 pieces = (2 + 8 + 10) = 20 inches yay!

Answer 2

1st piece - x
2nd piece - 4x
3rd piece - 5x


`x+4x+5x=20\\ 10x=20\\ x=2\\ 4x=4\cdot2=8\\ 5x=5\cdot2=10`

1st piece - 2 in
2nd piece - 8 in
3rd piece - 10 in