Question

A 20 in board is to be cut into 3 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 length of all three pieces

Answer 1

first piece: 2in

second piece: 8in

third piece: 10in

Explanation:

We have

first piece + second piece + third piece = 20

second piece = 4 * first piece = 4x

third piece = 5 * first piece = 5x

x + second piece + third piece = 20

plug 4x in for the second piece, 5x in for the third

x + 4x + 5x = 20

combine like terms

10x = 20

divide both sides by 10 to isolate x

x = 2

second piece = 4x = 8

third piece = 5x = 10