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?
M>2S,3S>4F,3F>M.Now we get
M>2S>(8/3)F.
S>(4/3)F>(4/9)M.
F>M/3>2S/3.
Substiute these in M+S+F=100, we get
M+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>25
S+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 20070814 05:52:15 