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

The answer to your question is x = 2, y = 8 and z = 10

Step-by-step explanation:

Data

Total length = 20 in

3 pieces, x = first piece

y = second piece

z = third piece

Process

1.- Write equations that help to solve this problem

             4x = y                          Equation l

             5x = z                          Equation ll

             x + y + z = 20               Equation lll

2.- Substitute equation l and ll in equation lll

            x + 4x + 5x = 20

3.- Solve for x

                        10x = 20

                            x = 20/10

                            x = 2 in

4.- Calculate y and z

                y = 4(2)

                y = 8 in

                z = 5(2)

               z = 10 in

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