# Bums need math, too

I was a goof-off in math class all through grades six, seven, eight, nine, and ten. That’s roughly pre-algebra through geometry and including college algebra. Most of the teachers along the way let the goofs goof off, and they focused their attention on serious students instead. We goofed around in the back of class and shouted disruptive answers while the teacher tried her best to carry the lesson.

Freshman geometry was my rock bottom.

Our classroom made for 30 was beyond capacity. More than 40 pubescent honors students sat shoulder-to-shoulder to study math right before or after lunch. My goof friends and I posted up in the back where we traded turns paying attention. We shared notes, homework, and sometimes even test answers.

Our most embarrassing claim to fame was to justify talking out as “math debating.”

Math came easy enough that I could goof off and pass most of the time. My parents must remember the parent-teacher conferences that went something like this: Brian’s low grade isn’t because he can’t do the work; it’s because he chooses not to do the work.

It wasn’t until my junior year of high school and trigonometry/pre-calculus that I finally settled down as a serious math student. My goof friends grew up, too. That was the first year I didn’t hear us lamenting about the unlikelihood we would ever use these lessons again in real life. And whether it took *me* becoming serious to finally recognize the seriousness in my math teacher, I think that was the first year I saw devotion in her eyes. She cared enough to pay attention to *every* student and reassured us that these skills would in fact be useful outside high school and even college.

Today I’m shopping foreign currency exchange rates. I only need a few hundred dollars to get me across the border where my bank card will then print money at any ATM for no fee and at the best rate. Until I cross, I must turn to currency exchangers for this service.

Exchangers compete with each other on rates and fees. Sometimes the highest rate isn’t the best deal if it is coupled with a fee. Other times it is. Banks and currency exchangers complicate the exchange for a reason: they know math and hope the customer doesn’t.

For example, Texas Currency Exchange quoted me a great rate of 12.68 Mexican pesos for every 1 US dollar. The next-best rate came from Frost Bank at 12.23 to 1. But TCE’s quote is complicated by an exchange fee of $3 that Frost doesn’t charge. The question is: where do these rates intersect?

You may remember word problems such as this from intermediate algebra. Surprise: solving systems of linear equations has a use beyond math class. The truth is that both of these rates offer the best exchange: one for large amounts and the other for small. Where exactly they equal each other is an answer found with math.

See if you can work the solution and post your answer to the comments if you dare. I’ll post my solution later.

EDIT: Of course you can cheat and estimate an answer by looking at the graph I posted. Here’s the math way to answer this problem:

- Create two equations, one to represent each currency exchange:

y = 12.23x

y = 12.68(x – 3) - Set the equations equal to each other and solve for the common variable:

12.68(x – 3) = 12.23x

12.68x – 3*12.68 = 12.23x

12.68x – 12.23x = 3*12.68

0.45x = 38.04

x = 38.04/0.45

x = 84.53 - Test the answer by substituting the result for x:

12.68(84.53 – 3) = 12.23*84.53

12.68*81.53 = 1033.80

1033.80 = 1033.80

This means that for exchanges less than $84.53 USD, the lower rate at Frost Bank without the fee is the better deal. For exchanges greater than $84.53, the higher rate with the fee at Texas Currency Exchange is the better deal. For exchanges equal to $84.53, both exchangers offer the same deal.