Cats and Dogs and Mice - Oh My!

RAY: So, here's the equation: D stands for dogs plus C stands for cats plus M stands for mice equals 100.

TOM: That's the equation.

RAY: And then 15 D, a dog costs 15 bucks plus 1 C, cats cost a buck. Plus 0.25 M. Now, as any eighth grader will tell you, you can't solve this because you have two equations and three unknowns, D, C and M.

Well, here's how I solved it. I figured it wasn't going to be five dogs because five dogs would eat up $75 and then you'd only have $25 with which to buy another 95 animals, and it wasn't going to work.

TOM: No.

RAY: And I knew it wasn't zero dogs because that was one of the conditions of the puzzler. So I changed the equation from three unknowns to two. And I wrote new equations. The first one of which is C plus 0.25M equals 85. That assumes one dog. And then the C plus M, now becomes 99. And you do that, and I solve for M.

TOM: Yeah, and what'd you get, what'd you get?

RAY: Eighteen and two thirds mice.

TOM: No good.

RAY: And if you then do it for two dogs, your equation becomes C plus 0.25M equals 70, and when you solve that equation you get a similarly unsatisfactory result. So this is kind of trial and error. And the correct answer turns out to be three dogs, 41 cats and 56 mice.

TOM: Yeah. That's good. I got that answer, too.

RAY: At what, 3:30 am?

TOM: No, I had the answer right away. I just kept thinking there was an elegant way of doing it.

RAY: I'm sure there is an elegant way of doing it.

TOM: There isn't.

RAY: Anyway, who's our winner?

TOM: The winner is Boyce Griffith from Oak Ridge, Tennessee.

[ Car Talk Puzzler ]