Alison has a piece of board 70 inches long. she cuts it into three pieces. the longest piece is twice the length of the middle sized piece, and the shortest piece is 10 inches shorter than the middle sized piece. find the length of the longest piece. let x = length of the middle sized piece.

X=lenght of the middle sized piece.
2x=lenght of the longest piece.
x-10=lenth of the sohtest piece.

we can suggest this equation:

(2x)+(x)+(x-10)=70
4x-10=70
4x=70+10
4x=80
x=80/4
x=20

therefore:
lenght of the middle sized piece:  x=20
lenght of the longest piece:  2x=2(20)=40
lenth of the sohtest piece:  x-10=20-10=10.

the length of the longest piece is 40 in.