Answer:
2'
Explanation:
An eleven-foot long board must be cut into three pieces so that one piece is 1-foot shorter than half the length of the longest piece and the other piece is 3 feet shorter than the longest piece. How long is the shortest piece?
board 1 = 0.5L - 1
board 2 = L - 3
board 3 = L
so:
(0.5L - 1) + (L - 3) + L = 11'
0.5L - 1 + L - 3 + L = 11'
combine L on left side:
2.5L - 4 = 11
add4 from both sides:
2.5L - 4 + 4 = 11 + 4
2.5L = 15
divide both sides by 2.5:
2.5L/2.5 = 15/2.5
L = 6
Formula for boards are, substitute in L = 6:
board 1 = 0.5L - 1
= 0.5(6) - 1
= 3 - 1
= 2'
board 2 = L - 3
= 6 - 3
3'
board 3 = L
= 6
shortest board is board 1 at 2'