Here's the question:
A chicken and-a-half lays an egg and-a-half in a day and-a-half. Assuming eggs are fungible and fully divisible, how many eggs does one chicken lay in a day?
Here's what I've done so far:
1.5 chicken 1.5 eggs in 1.5 days. Multiplying that by 2 chickens gives: 3 chickens 3 eggs in 1.5 days. Dividing that by 3 to get for 1 chicken gives: 1 chicken 1 eggs in 1.5 days
I'm not sure how to get for 1 day though.
On
A chicken and-a-half lays an egg and-a-half in a day and-a-half.
So we have $$ 1.5 \,\text{chicken} \times 1.5 \,\text{d} \times r = 1.5 \,\text{egg} $$ where $r$ is the production rate: $$ r = \frac{1.5}{1.5 \times 1.5} \frac{\text{egg}}{\text{chicken}\times\text{d}} = \frac{2}{3} \frac{\text{egg}}{\text{chicken}\times\text{d}} $$
Assuming eggs are fungible and fully divisible, how many eggs does one chicken lay in a day?
After looking up fungible (= all eggs are the same value, there are no golden eggs in between :) we see $$ 1 \,\text{chicken} \times 1 \,\text{d} \times \frac{2}{3} \frac{\text{egg}}{\text{chicken}\times\text{d}} = \frac{2}{3} \,\text{egg} $$
"A chicken and-a-half lays an egg and-a-half in a day and-a-half"
$\iff$
"A chicken and-a-half lays an egg in a day"
$\iff$
"A chicken lays $\frac{2}{3}$ of an egg in a day"
The key is to approach the problem logically and clean up the variables one at a time.