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A man wants to cut three lengths from a single piece of cloth of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest piece of cloth if the third piece is to at least 5 cm longer than the second.

Text Solution

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Let the length of the shortest piece be x cm. Then, second length `=(x+3)` cm and third length `= 2x ` cm.
`thereforex +(x+3)+2xle91]and 2xge(x+3)+5`
`rArr 4x+3le91 and2xgex+8`
`rArr 4x le91-3and 2x-xge8`
`rArr 4x le88 and x ge8`
`rArrx le22 and x ge 8`
`rArrx le22 and x ge 8`
Hence, the length of the shortest piece is to be greater than or equal to 8 but less than to 22.
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Explore conceptually related problems

A man wants to cut three lenghts from a single piece of board of length 91 cm . The secound length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second? [Hint : If x is length of the shortest board, then x, ( x+3) and 2x are the lengths of the second and third piece, respectively. Thus , x + (x + 3 ) +3x le 91 and 2x ge (x + 3 ) + 5] .

A man wants to cut three lengths from a single piece of board of length 91cm The second length is to be 3cm longer than the shortest and the third length is to be twice as long as the shortest.What are the possible lengths of the shortest.What are the possible lengths of least 5cm longer than the second?

Knowledge Check

  • A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest . The possible length of the shortest board, if the third piece is to be at least 5 cm longer than the second ,is

    A
    less than 8 cm
    B
    greater than or equal to 8 cm but less than or equal to 22 cm
    C
    less than 22 cm
    D
    greater than 22 cm

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