Word problem from an old book

Problem: A boy was sent for $1.20 worth of eggs. On his way home he broke five eggs and thereby he paid twenty-four cents more per dozen of eggs. How many eggs did he buy?

How would one go about setting up this problem?

n = number of eggs
x = price of 1 egg

n*x = 1.20 ==> x=1.20/n -- (1)

note that if each dozen eggs cost 24c more, each eggs cost 2 cents more (0.02$)

1.20 /(n-5) = 0.02+x

==> 1.20 = (n-5)*(0.02+x) -- (2)


replacing (1) in (2), you get:

1.20 = (n-5)*(0.02+1.20/n)
1.20 = 0.02n + 1.20 - 0.1 - 6/n
0 = 0.02n -0.1 - 6/n

If you multiply by 50n to simplify:

0 = n^2 - 50n - 300

solve with: http://www.ajdesigner.com/phpquadraticequation/quadraticequation.php

positive root: 20 eggs!

so you had 20 eggs at 6c each...

since you broke 5, you ended up with 15 eggs...1.20/15 = 0.08... 8c, 2c more!

When