Subj:.....The Price Of Eggs (S638)            From the book              "More Mathematical Puzzles              of Sam Loyd"            Edited by Martin Gardner            From: Dover Publications in 1960

Drawing from Karen's Art Page

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"I paid twelve cents for the eggs I bought from the grocer,"  explained the cook, "but I made him throw in two extra eggs  because they were so little.  That made the lot cost just  one cent per dozen less than the first asking price."  How many eggs did the cook buy? . . Finger pointing down from darrell94590 on 1/2/2006 .       Drawing from Ripleys-Believe It Or Not ..               THE SOLUTION   The cook bought sixteen eggs, but the grocer threw in two extra eggs, making eighteen in all. ¤»¥«¤»§«¤»¥«¤»§«¤»¥«¤»§«¤»¥«¤»§«¤»¥«¤»§«¤»¥«¤»§«¤»¥«¤ My solution is the following: Let X = the original number of eggs The equation becomes    Original price per dozen - One  =  New price per dozen    Creating the equation from the word equation yields    12               12                      144             144   _____  -  1  =  _____  which reduces to  _____  -  1  =  _____     X             X + 2                      X             X + 2    __             _____    12              12    Multiplying both sides of the equation by the common    denominator of  X ( X + 2 ) yields    144 ( X + 2 )  -  1 X ( X + 2 )  =  144 X    Multiplying    144 X  +  288  -  X²  +  2 X  =  144 X    Moving everything to the right side of the equation yields    0  =  X²  -  2 X  - 288    Factoring    0  =  ( X - 18 ) ( X + 16 )    Setting each factor equal to zero yields    X  =  16  or  - 18    Therefore the answer is the cook bought sixteen eggs.

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