Challenge Level

Well done to Amina from Greenacre Public School, Australia and Carl who sent us their solutions to this problem.

Amina found the ratio between the different organisms in the food chain and used it to find the answer to the first part or the problem:

$$ \begin{align}

\begin{array}{ccccccc}

\text{Bushes} &:& \text{Caterpillars}&:& \text{Birds}&:& \text{Wildcats}\\

1 & :& 30 & :& 3 & :& 1 \\

500 & :& 15000 & :& 1500 & :& 500

\end{array}

\end{align}

$$Therefore, if there are $500$ bushes, there will be $15000$ caterpillars, $1500$ birds and $500$ wildcats.

Carl sent us the following solutions to the other parts of the problem:

If the wildcats became vegetarian and ate the bush, they would get $75\%$ of the energy instead. So the wildcats could get $\frac{0.75-0.421875}{0.421875}=\frac{7}{9}=77.\dot{7}\%$ more energy by eating the bushes if they were vegetarian.

$$ \frac{10000}{10} = 1000 \text{ birds}\\

\frac{1000}{3} = 333 \text{ wildcats} $$This means that $500-333=167$ wildcats would starve due to a lack of food.