Question

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.

Answer 1

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.