Question

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

Answer 1

I got `1/6` of a pound.

Explanation:

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

Answer 2

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

Explanation:

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"`