Question

A farmer has a stock of food enough to feed $28$ animals for nine days. He buys $8$ more animals which take same quantity food. How long would the food last now?

Answer 1

The statement " $y$ varies inversely as $x$ means that when $x$ increases, $y$ decreases by the same factor. In other words, the expression $xy$ is constant:

$xy=k$

where $k$ is the constant of variation.

Let the number of animals be $x$ and the number of days be $y$.

Here, it is given that $x=28$ animals are feeded in $y=9$ days, therefore,

$xy=k\Rightarrow 28\times 9=k\Rightarrow k=252$

Thus, the general equation is $xy=252$.

Since $x=28+8=36$, therefore,

$36y=252\Rightarrow y=\frac{252}{36}=7$

Hence, the food lasts for $7$ days.