# The elephant diet

Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day

One of the elephants in the zoo is on a special diet.

Every day, the elephant eats as much carrot mash as the rabbitÂ eats in 1 year (365 days).

The rabbit eats the same quantity of carrot every day.

Together, in one day, the elephant and rabbit eat 122 kilograms of carrot.

How many kilograms of carrot does the rabbit eat in one day?

*This problem is adapted from the World Mathematics Championships*

**Answer**:Â $\frac13$ kg

**Using words**

Elephant portion = 365 rabbit portions

Rabbit portion = 1 rabbit portion

Total = 366 rabbit portions

366 rabbit portions = 122 kg

1 rabbit portion = 122$\div$366 = $\frac13$ kg of carrots.

**Using algebra**

Suppose the rabbit eats $r$ kg of carrots each day.

Then the elephant eats $365r$ kg of carrots each day.

Together, they eat 122 kg of carrots, so $$\begin{align} r+365r&=122\\

\Rightarrow 366r&=122\\

\Rightarrow r&=\tfrac{122}{366}\\

\Rightarrow r&=\tfrac13\end{align}$$