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A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest board if the third piece is to be at least 5 cm longer than the second?
  • a)
    5 ≤ × ≤ 91
  • b)
    3 ≤ × ≤ 5
  • c)
    3 ≤ × ≤ 91
  • d)
    8 ≤ × ≤ 22
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A man wants to cut three lengths from a single piece of board of lengt...
Let x be the length of the shortest board.
The second length is x+3.
The third length is 2x.
The third length is at least 5 cm longer than the second: 2x ≥ (x+3)+5
2x ≥ x+8
x ≥ 8
The possible lengths for the shortest board are x ≥ 8. Answer: \boxed{8}.
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Community Answer
A man wants to cut three lengths from a single piece of board of lengt...
Let the length of the shortest piece be x cm. Then, length of the second piece and the third piece are (x + 3) cm and 2x cm respectively.
Since the three lengths are to be cut from a single piece of board of length 91 cm,
x cm + (x + 3) cm + 2x cm ≤ 91 cm
⇒ 4x + 3 ≤ 91
⇒ 4x ≤ 91 ­– 3
⇒ 4x ≤ 88
⇒ x ≤ 22   ...(1)
Also, the third piece is at least 5 cm longer than the second piece.
∴ 2x ≥ (x + 3) + 5
⇒ 2x ≥ x + 8
⇒ x ≥ 8 …(2)
From (1) and (2), we obtain
8 ≤ x ≤ 22
Thus, the possible length of the shortest board is greater than or equal to 8 cm but less than or equal to 22 cm.
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A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest board if the third piece is to be at least 5 cm longer than the second?a)5≤×≤ 91b)3≤×≤ 5c)3≤×≤ 91d)8≤×≤ 22Correct answer is option 'D'. Can you explain this answer?
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