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 Compendium, Book And Novel (Posted on 2007-08-11)
Trevor has recently purchased a classical music compendium, a science book and a fiction novel from his neighborhood bookstore for a total of \$100. It is known that:

(I) The music compendium costs more than twice the science book.

(II) Three copies of the science book cost more than four copies of the fiction novel.

(III) Three copies of the fiction novel cost more than the music compendium.

Given that all prices are whole numbers of dollars, how much does each item cost?

 See The Solution Submitted by K Sengupta Rating: 2.6667 (3 votes)

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 Solution Comment 5 of 5 |
`M>2S,3S>4F,3F>M.Now we getM>2S>(8/3)F.S>(4/3)F>(4/9)M.F>M/3>2S/3.Substiute these in M+S+F=100, we getM+M/2+(3/8)M>100 => M>160/3=53.33.M+(4/9)M+M/3<100 => M<56.25 => M={54,55,56}S+(3/4)S+(9/4)S>100 => S>25S+2S+2S/3 <100 => 11S/3>100 =>S<300/11 => S<27.27.`
S={26,27}

F+3F+(3/2)F>100 => F>200/11 => F>18.18..
F+(8/3)F+(4/3)F<100 =>F<20 => F=19

But M+S+F=100 => M+S=81. Now Consider the values of M,S
M=54, S=27  is not  possible as M>2S
Hence M=55,S=26 is the only solution for M+S=81.
Hence {M,S,F}={55,26,19}

 Posted by Praneeth on 2007-08-14 05:52:15

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