If eggs are $2.00 a dozen and cost $1.00 per pound, how much does an egg weigh?

If 12 eggs costs #$2.00# this means that one egg costs:
#2/12=1/6# of a dollar.
Now 1 pound of eggs will contain:
#1/(1/6)=6# eggs each one weighting:
#1/6# of a pound.

or:

If 12 eggs costs #$2# it means that 6 eggs will cost #$1#; but this is exactly the price of 1 pound of eggs! So in 1 pound we have 6 eggs each one wighting:
#1/6# of a pound

Depending on the level of precision the weights of individual eggs will differ.

Assumption: All the eggs are of the same weight.

Let weight be #w#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Considering the method")#

#color(brown)("You can treat units of measurement the same way you do numbers")#
Looking at the units of measurement to give us what we need.

we have #("cost")/("count")" and "("cost")/("weight")#

Need to determine #("weight")/("count") = w/1#

So we need to turn the second one upside down and then multiply:

Target is: #(cancel("cost"))/("count")xx("weight")/(cancel("cost")) = ("weight")/("count")#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#($2)/("1 dozen eggs") xx("1 lb")/($1)#

But 1 dozen eggs is 12

#color(red)(($2)/("12 eggs")) xxcolor(green)(("1 lb")/($1))#

Using the principle as in this example: #2xx4# is the same as
#4xx2#

#color(green)((color(red)($2))/($1)xx(1lb)/(color(red)("12 eggs")))#

#$/$xx2/1xx1/12xx(lb)/("egg")#

Treat #$/$# as 1

#2/12 (lb)/("egg")#

But there are 16 oz in 1 lb

#2/12 xx16color(white)(.) (oz)/("egg")#

#2/(cancel(12)^3) xxcancel(16)^4color(white)(.) (oz)/("egg")#

#8/3 ("oz")/("egg")#

Each egg weighs #2 2/3" ounces"#