Mathnasium Word Problem: Toucan!

The Mathnasium word problem menagerie is getting bigger and bigger, and this week, we're all about a beautiful tropical South American bird with a formidable beak and lots of character! On this fine, feathery Word Problem Wednesday, try solving our toucan word problem and check below for the answer.

A biologist is monitoring a flock of toucans. The biologist determines that the number of toucans in the flock can be estimated using the function f(n) = 22 + 3n, wherein n is the number of toucan nests that the biologist counts in the flock’s territory. If the biologist counts 5 nests, what is the estimated number of toucans?

The toucan's distinctively huge beak makes it instantly recognizable. For many of us, our first exposure to toucans may have been "Toucan Sam" who is the mascot for Froot Loops breakfast cereal. That famous beak is ⅓ the length of the bird! That's huge, but despite it's size, the beak is quite light since it's full of air pockets. Amazingly, the toucan regulates its temperature by controlling blood flow to its beak where the heat is lost through those air pockets. More blood flow means more heat loss. At night, the toucan sleeps with its beak tucked under its wing to keep warm. That's a pretty cool fact!

Of course, the beak's other important function is for feeding. The toucan uses its length to its advantage to reach fruit far away on branches that would not otherwise bear its weight. Other than a primary diet of fruit, toucans also eat insects, and sometimes young birds, eggs, or lizards.

It's unfortunate that toucans are a favorite of the pet trade, with many wild birds trapped for the pet market. Another quick math question. If a toucan's beak is 7½ inches long, how long is the whole bird (from beak to tail)? Remember that the beak is ⅓ of the bird! So, if you answered 22½ inches, you're right. We like to do it this way, 7 x 3 + ½ x3 = 21 + 1½ = 22½inches. That's almost 2 feet. It's a huge bird that does not make a great house pet. Leave wild animals in the wild where they belong.

Now for the answer. The function f(n) = 22 + 3n states that a flock has at least 22 toucans and each nest increases the flock by 3 more toucans. So, when n=5, f(5) = 22 + 3(5) = 22 + 15 = 37 toucans. Remember PEMDAS, multiply first then add.

And we leave you with this...

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Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee
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Photo:Toucan Toco in Iguazu.jpg - Wikimedia Commons