We love learning new words here at Bedtime Math, and we just discovered a great one, “porcupette“:” it’s a baby porcupine. As cuddly as porcupines look, we also know they’re extremely prickly: a porcupine can have up to 30,000 quills! And those quills can be up to 5 inches long. Luckily porcupines can’t actively shoot their quills at you, but if you scare a porcupine while touching it, it will let them loose and their points will stick into your hand. The porcupine is the 3rd-largest rodent, after the capybara and beaver, and it isn’t the fastest-moving animal, but when scared they can break into a gallop. Some weigh as much as 60 pounds, but other types are as small as 2 pounds, making it a very huggable, holdable pet – if you’re sure it won’t prickle you with its quills.
Wee ones: If porcupines are the 3rd largest rodent, how many rodents are bigger than they are?
Little kids: If a family of 2 porcupines and their 5 baby porcupettes wanders into your yard, how many prickly animals is that? Bonus: If you wanted to see a dozen prickly animals total, how many more porcupettes would have to show up?
Big kids: Who weighs more, you or a 60-pound porcupine – and by how much? Bonus: A human head has about 100,000 hairs on it. How many more hairs do you have than a porcupine’s 30,000 quills?
The sky’s the limit: If you’re picking pets from some 40-animal mix of porcupines and porcupettes, and you choose 1/4 of the porcupines and 1/6 of the porcupettes, how many of each do you have if you end up with 7 animals?
Wee ones: 2 other rodents.
Little kids: 7 animals. Bonus: 5 more porcupettes.
Big kids: Different for everyone…subtract your weight in pounds from 60, or subtract 60 from your weight. Bonus: 70,000 more.
The sky’s the limit: You’ll end up with 1 porcupine and 6 porcupettes. If we call the two sizes P and p, we know:
P + p = 40
1/4P + 1/6p = 7
Substituting, we get
1/4 x (40 – p) + 1/6p = 7
so 10 – 1/4p +1/6p = 7
Subtracting terms from both sides, you can flip it around to get
10 – 7 = 3 = 1/4p – 1/6p
Multiply through by 12 to simplify…
36 = 3p – 2p = p
So there are 36 porcupettes, and therefore 4 porcupines. You choose 1/6 of the little guys and 1/4 of the big guys, giving you 1 porcupine and 6 porcupettes.