Question

If an island's only residents are penguins and bears, and if there are 21 heads and 50 feet on the island, how many penguins and how many bears are on the island?

Answer 1

Answer:

The number of penguins on the island is 17 and the number of bears on the island is 4.

Step-by-step explanation:

We are given that an island's only residents are penguins and bears, and if there are 21 heads and 50 feet on the island.

Let the number of penguins on the island be 'x' and the number of bears on the island be 'y'.

Also, we know that bears and penguins both have one head, and the bear has 4 feet and the penguin has 2 feet.

So, according to the question;

• The first condition states that there are 21 heads, that means;

                             x + y = 21  

                             x = 21 - y  ---------------- [equation 1]

• The second condition states that there are 50 feet on the island, that means;

                            2x + 4y = 50

                             x + 2y = 25

                            21 - y + 2y = 25    {from equation 1}

                            y = 25 - 21

                            y = 4

Now, putting the value of y in equation 1, we get;

                           x = 21 - y

                           x = 21 - 4 = 17

Hence, the number of penguins on the island is 17 and the number of bears on the island is 4.