#2             94.  NOT A LEG TO STAND ON           

As Ella and Dulcie were leaving the zoo, Ella said, “I did like the way the emus and deer were all together! Did you count them? Between them they had 24 eyes and 38 legs!”

“Actually, I was more interested in the jungle house,” said Dulcie. I counted 16 heads and 30 legs there!”

“I don’t get it,” said Ella after a while. “You must have made a mistake.”

“No,” said Dulcie. “In fact, there were twice as many four-footed creatures as there were two-footed creatures.”

How many deer, emus and jungle creatures were there in the zoo?

Hints and strategies

Hint 1                Hint 2              Solution               Extensions
HINT 1

Try a little algebra for the emu and deer, or some trial and error.
HINT 2

For the jungle creatures you might like to be a little creative. The term ‘jungle creatures’ is a bit non-specific!
SOLUTION

Suppose first that there are d deer and e emus.

Then 2d + 2e = 24, and 4d + 2e = 38.

Solving, we get d = 7 and e = 5.

In the jungle enclosure, suppose there are f four-footed creatures and t two-footed creatures.

Then  f  = 2t and as a first try,  f + t = 16, and 4f + 2t = 30.

This information just leads to a contradiction. However, if there were also s snakes, we would get

f = 2t, f + t + s = 16, and 4f + 2t = 30, leading to t = 3, f = 6 and s = 7.
i.e. 3 two-footed, 6 four-footed and 7 snakes.
EXTENSIONS

You could obviously try varying the numbers in this problem. You might also think about the things being counted. For example, if you were counting horns, you might put in some unicorns, and even the zoo van!