Question

The cost of producing a chocobar varies inversely with the number of chocobars produced. If 400 chocobars are produced, then the cost is $\$2$ each. If 1600 chocobars are produced, then the cost(in cents) of one bar is .

Answer 1

Let the cost of producing a chocobar be $C$ and the number of chocobars produced be $n$.
$\text{Given that}C\propto \frac{1}{n}$
$\Rightarrow C=\frac{k}{n}$ (let k be a constant)
We know that $400$ chocolates are produced at a cost of $\$2$ each.
$\Rightarrow 2=\frac{k}{400}\Rightarrow k=800$

$\Rightarrow C=\frac{800}{n}$

If $1600$ chocobars are produced, then the cost of each chocobar is

$\Rightarrow C=\frac{800}{1600}=\$0.5=50\text{cents}$