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Brainteaser: Animal equations

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Difficulty: Tricky

In this puzzle, each Aussie animal stands for a number. Each animal represents the same number throughout the puzzle. Can you use the first three mathematical equations to figure out the answer to the last equation?

Need a hint?

The first equation only has one type of animal, so it’s a really good place to start. If you can work out what a kangaroo is worth, you can use that for the rest of the equations.

For mathematical equations, you can make changes to an equation, and as long as you do the same thing on both sides of the equal sign, it will remain true. For example, say you had:

3 x orca = 15, this equation can be simplified by dividing both sides by 3.

3 x orca ÷ 3 = 15 ÷ 3, dividing by 3 cancels out the multiplication by 3, so you end up with:
orca = 5

Finally, remember that the order of operations rule tells you to multiply before you add.

The kangaroo stands for 3. The echidna stands for 2. And the koala stands for 4. So the last equation is 4 + 2 x 3, which equals 10.

Let’s start with the first equation. Multiplying three kangaroos together might seem hard, but it’s the only equation with only one symbol.

A good way to work it out is guessing and checking. 2 x 2 x 2 is too small, and 4 x 4 x 4 is too big. You might also spot the clue that since 27 is odd, kangaroo must also be odd. In any case, you’ll soon come to the conclusion that 3 x 3 x 3 = 27 and kangaroo is therefore 3.

In our next equation, we can substitute three in for the kangaroo. This gives us:

3 x echidna x echidna = 12

We can write echidna x echidna as echidna squared.

3 x echidna2 = 12

Next, you can make changes to an equation, and as long as you do the same thing on both sides of the equal sign, it will remain true. In this case, we can divide both sides by 3:
3 x echidna2 ÷ 3 = 12 ÷ 3, here we divide by 3 to take out the multiplication by 3
echidna2 = 4

What number squared equals 4? Two times two equals four, so one echidna stands for 2.

We can use our third equation to find the value of a koala. Start by substituting the numbers you know:

3 x 2 x koala x koala = 96, which equals:

6 x koala2 = 96

Next we can make changes to both sides of the equation by dividing both sides by 6.

6 x koala2 ÷ 6 = 96 ÷ 6
koala2 = 16

What number squared equals 16? We know 2 squared is 4, three squared is 9, and four squared is 16.

This means that the koala stands for 4.

Now we can combine this knowledge with the last equation:
koala + echidna x kangaroo = ?

4 + 2 x 3 = ?

Remember that with the order of operations, we do multiplication before addition:

4 + 6 = ?

And now we have our answer!

4 + 6 = 10.

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