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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?

1 Answer

4 votes

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'

User Hosjay
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