# Algebraically Challenged

I was helping the girls with their Algebra II homework last night, specifically with a Challenge question that was stumping them. It looked something like this (actual values changed so as to avoid giving away the textbook solution):

CHALLENGE: For any three distinct numbers, a, b, and c, a$b$c is defined as $a\b\c = \frac{-a-b-c}{c-b-a}$. Find -5$-8$10.

Forget, for a moment, that the notation a$b$c is not something you’re going to find in real-world math anywhere that isn’t an academic textbook. And let’s also forget, for a moment, that this isn’t even really an algebra problem, let alone Algebra II. (It might qualify as pre-algebra, but only just barely). There’s no balancing an equation, no solving for a variable, nothing that makes this anything more than simple addition/subtraction and division. Once you clear out all the confusing words around the problem, what you’re left with is a basic substitution problem. The problem statement gives you a$b$c = -5$-8$10, which works out to a = -5, b = -8, and c = 10. From there, it’s just a matter of subbing those numbers into the equation and solving (without overlooking all the double negatives, which is really the only tricky part of the whole equation).

So as it turns out, the “challenge” in this question isn’t the problem itself. It’s in interpreting the author’s cryptic and backwards presentation of the problem, which seems designed to do nothing more than make a basic third-grade math problem extravagantly more confusing. I’m trying to decide if this should be a commentary on the quality of math education our kids are receiving in the US now.