# Circus Math

##### Jan 29, 2022

It's time for this week's puzzler! Now this one is mathematical.

I'll try to state it as succinctly as Mildred Stanger did. She's the one who submitted this puzzle.

Okay, here we be. 100 people attend a circus. The total admissions comes to exactly \$100.

Got that? 100 people altogether paid \$100. Right now if they paid a buck apiece, that would be approximately 100 people for \$100.

But, that would be too easy. Right? The admission charges are thus:

Oh and get a pencil now because you may not remember the details of this puzzler and a lot is at stake here. You might want to write this down.

The charges are \$5 per man, \$2 per woman, and 10 cents per child. That's one thin dime for any kid.

What was the number of men, women, and children who attended?

Now this may sound simple, but you will soon find out that you have written down three equations and you have three unknowns.

100 people attend the circus. Not a very big turnout but it's a small circle flea circus.

The total admissions come to exactly \$100. The charges for admissions were as follows \$5 per man, \$2 per woman, and 10 cents per child under the age of 12.

How many men women and children attended? Piece of cake, you say you write down your equations, x + y + z! X being men, y being women z being children. (Now here my brother convinced me it was better to use mnemonic variables, so let's say it's m for men, w for women, and c for children.)

Then we have 5m, plus 2w, and 1c. And you solve for M, W, or C. But you will soon come to realize that you have two equations and three unknowns. But as Mildred suggested, this is not as simple as it looks, until you figure out the little trick. And as soon as you see the trick, as soon as you see that you have the basic eureka, aha moment!

And the key is that the children must must come in increments of 10. Otherwise, you'd have a number that won't work.

I mean, if there were six kids, that would be 60 cents, and it would be impossible to solve because you can't have \$100 if you have 60 cents hanging on the end someplace, right?

So let's say 10 kids came in.

So your first equation would be 5m + 2w = \$99, and m + w = 90 people. So now when I solve that, it doesn't come out right.

So you keep doing you do another one, 5m + 2y = 98 and m + w = 80, and that doesn't work either.

So you keep going and going, and finally, finally when you stick in 70 kids, you come up with 70 kids, 19 women, and 11 men. And that adds up to 100 people and \$100.

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