10 foot board is cut into three pieces

Question

10 foot board cut into three pieces. The second piece is 1 foot longer than the 1 st piece. The third piece is 3 feet longer than the first piece. Find the length of each piece.

Answer 1

Second piece is 1 foot longer than first piece: S=1+F

Third piece is 3 feet longer than first piece: T=3+F

It's a 10 foot board: F+S+T=10

substitute the two equations into the last to get

F+1+F+3+F=10

3F=6

F=2

S+1+F=1+2=3

T=3+F=3+2=5

Lengths of the 3 pieces are 2 feet, 3 feet, and 5 feet