Math CentralQuandaries & Queries


Question from Sophia, a parent:

While visiting a pet store, you notice that there are only birds and cats in the cages. You can't help but wonder how many of each animal there is in the yard. But when you ask the store manager how many of each animal he has, he refuses to give a direct answer. He says there are 16 animal heads and 42 animal feet. How many birds and cats are there in the pet store? It said to show all your work. Explain in words how you found your answer. Tell why you took the steps you did to solve the problem.

Hi Sophia,

I like this problem because you can solve it by constructing something or imagining you are constructing something.

Suppose you have 16 marshmallows (heads) and 42 toothpicks (feet). If you put two toothpicks in a marshmallow you have a bird and if you put 4 toothpicks in a marshmallow you have a cat. Start by putting two toothpicks in each marshmallow. How many toothpicks did you use? How many are left over? Take two of the left over toothpicks and put them into a bird to turn it into a cat. Continue until you have used all the left over toothpicks. How many cats did you make? How many birds are there?

I hope this helps,

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