A 50 -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.

1. Let

x = first piece

y = second piece

z = third piece

2. Arrange it into an equation

x + y + z = 50

3. The second piece is 4 times as long as the first piece so 4x = y.

The third piece is 5 times as long as the first piece so 5x = z

4. Now substitute the values

x + (4x) + (5x) = 50

5. Simplifying makes the equation into 10x = 50

6. Do the opposite of multiplying to get rid of the 10 which is dividing. Divide 50 by 10.

x = 50/10

x = 5

7. Now substitute x in 4x and 5x

4 * 5 = 20

5 * 5 = 25

8.

x = 5

y = 20

z = 25