Cheetahs are big cats covered with cool-looking spots. So how many spots do they have? Scientists have tried to guess, but one said 456 spots, while another said between 2,000 and 3.000. So we at Bedtime Math tried counting spots on a picture of a cheetah. We counted 460 on one side, which would be 920 for the whole cat. Here’s a trick for counting lots of things: count the number in one little chunk, then guess how many of those chunks cover the whole area!

*Wee ones:* If you count 7 cheetah spots and then keep counting, what are the next 2 numbers you say?

*Little kids:* If you count 60 spots on a cheetah in sets of 10, what numbers do you say? *Bonus:* At least how many more sets would you have to count to say 90?

*Big kids:* If you’ve counted 20 spots in one patch and there are 4 of those patches on the cheetah’s right side, how many spots would that come to? *Bonus:* If the cheetah’s front right leg has 56 spots, the back right leg has 86, and the front left leg is exactly in between, how many does the front left leg have?

*The sky’s the limit:* Suppose 3 cheetahs have different numbers of spots. Chiquita and Chuck have 50 spots together; Chuck and Chandra have 90 spots together; and Chiquita and Chandra have 60 spots together, how many spots does each cheetah have?

Answers:

*Wee ones:* 8 and 9.

*Little kids:* 10, 20, 30, 40, 50, 60. *Bonus:* At least 3 more sets.

*Big kids:* 80 spots. *Bonus:* 71 spots (15 more than one leg, 15 less than the other, since they are 30 apart and 15 is 1/2 of 30).

*The sky’s the limit:* Chiquita has 10, Chuck has 40, and Chandra has 50. If Chiquita + Chuck have 50 and Chiquita + Chandra have 60, then Chandra must have 10 more than Chuck. Chuck and Chandra have 90 together, which means if they had an equal number, they’d have 80, giving each of them 40. So Chuck has 40, Chandra has 10 more (50), and Chiquita has 60 minus that, or 10. If you want to do this with formal algebra, for cheetahs a, b and c:

a + b = 50 so b = 50 – a

b + c = 90

a + c = 60

Substituting into the 2nd equation, we get

(50 – a) + c = 90, so

c – a = 40 and c = 40 + a

And we know a + c = 60, so

a + (40 + a) = 60

2a + 40 = 60

2a = 20

a = 10, so b = 40 and c = 50.