May 14, 2020

We usually don’t think of cats and dogs as being good friends. In fact, when people argue with each other, we say they’re “fighting like cats and dogs.” But the San Diego Zoo has figured out that dogs can be special friends with the fastest cats out there: cheetahs! Cheetahs get nervous easily, so it’s hard for them when they first move to the zoo — new foods, strange sounds, lots of people. So the zoo started giving each new cheetah cub a puppy dog as a “buddy.” The dog helps the cheetah feel safe. Because they grow up together, the cheetah and dog become great friends. They don’t know any better!

*Wee ones:* People are animals, too. How many animals are completely in the photo?

*Little kids:* How many legs do that cheetah and dog have together? *Bonus:* If you took both of them for a walk, how many more legs than you would your pets have together?

*Big kids:* If the zoo has twice as many cheetahs as buddy dogs, and there are 18 animals altogether, how many of each do they have? (*Hint if needed:* How many cheetahs does each dog have to itself?) *Bonus: *If there are 3 cheetahs named Antsy, Beastie and Charlie, and 3 dogs named Daisy, Elbert and Finn, how many different ways can the cheetahs and dogs be paired up as buddies?

*The sky’s the limit:* If you have 3 times as many cheetahs as dogs, but adding 5 cheetahs and 5 dogs would give you just twice as many cheetahs as dogs, how many of each animal do you have?

Answers:

*Wee ones:* 3 animals: 1 cheetah, 1 dog, 1 person.

*Little kids:* 8 legs. *Bonus:* 6 more legs, since they have 8 and you have only 2.

*Big kids:* 12 cheetahs and 6 dogs. Each dog gets 2 cheetahs, making sets of 3…and in 18 there are 6 sets. *Bonus: *6 ways. If A pairs with D, then you can have B-E and C-F, or B-F and C-E, so those are 2 ways. Then A can pair with E, giving us B-D and C-F or B-F and C-D. Finally, we have A-F with B-D and C-E or B-E and C-D.

*The sky’s the limit:* 15 cheetahs and 5 dogs to start. A quick way to solve this is with algebra: if we start with c cheetahs and d dogs, we have:

c = 3d and after adding to the piles, c + 5 = 2 x (d + 5)

Substituting, that means 3d + 5 = 2 x (d + 5)

3d + 5 = 2d + 10

If 3d + 5 = 2d + 10, we can subtract 5 from both sides…

3d = 2d + 5

and then subtract 2 d from each side, giving us

d = 5

So we have 5 dogs, and then three times that gives us 15 cheetahs.

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.

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