Two Turkeys

Date: 10/07/97 at 22:22:43
From: sarah guilmain
Subject: Logic problem

Together, two turkeys weigh 20 pounds, says the butcher.  The little 
fellow sells for two cents a pound more than the big bird.

Mrs. Smith bought the little one for 82 cents and Mrs. Brown paid 2.96 
cents for the big turkey.  How much did each turkey weigh?

Date: 10/09/97 at 13:08:37
From: Doctor Rob
Subject: Re: Logic problem

Let the smaller turkey weigh w pounds and the larger one W pounds.
Then the smaller turkey sells for 82/w cents per pound, and the 
larger one for 296/W cents per pound.  Then we get the equations

          W + w = 20
   82/w - 296/W = 2

Multiply the second equation by w*W on both sides to get rid of
fractions. Solve the first equation for w in terms of W, and 
substitute it into the result of the last sentence. This will give 
you one quadratic equation in the unknown W. Solve it for W, but 
one of the two solutions will be nonsensical, and must be discarded.  
The other gives you the answer for W, and hence for w.

You can finish the details.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/