Birdseed Formula

Date: 5 Jun 1995 22:01:46 -0400
From: Angela
Subject: Birdseed Formula

Someone has 3 dollars and wants to buy two kinds of bird seed 
(one is $1.49/lb. and the other is $2.88/lb.) with it (and does not 
have the extra change for 6% tax).  What is the formula for figuring 
out how much of each seed she can get?

Date: 6 Jun 1995 10:54:52 -0400
From: Dr. Ken
Subject: Birdseed Formula

Hello there!

I think the first thing I'd do in this problem is convert each of the two
prices to what they'll amount to after you tack on the tax.  Since it's 6%,
the two prices will be 1.06*1.49 = $1.58/lb and 1.06*2.88 = $3.05/lb.  Then
assuming she wants to spend her whole wad of 3 dollars, the amount of money
she spends on one kind plus the amount of money she spends on the other kind
should be a total of 3 dollars.  That gives us the following equation, where
x and y are the two kinds of seed:

x*1.58 + y*3.05 = 3

The way you'd use this equation is like this: if you know you want 1/2 pound
of the first kind of birdseed (ie. x=1/2), you plug that in and get 

.79 + y*3.05 = 3
y*3.05 = 2.21
y = .725 pounds of the second kind.

Thanks for the question!

-K