A50-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