The elephant diet
Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day
Age
11 to 14
Challenge level
Problem
One of the elephants in the zoo is on a special diet.
Every day, the elephant eats as much carrot mash as the rabbit 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
Student Solutions
Answer: $\frac13$ 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 $$\begin{align} r+365r&=122\\
\Rightarrow 366r&=122\\
\Rightarrow r&=\tfrac{122}{366}\\
\Rightarrow r&=\tfrac13\end{align}$$