I remember high school. Not fondly, but I do. One of the things I remember in particular were incessant complaints along the lines of "when will we ever use this stuff?"

Well my friend (working in the "real" world) messaged me the other day with a math question directly related to her job, and I thought I'd put my explanation up on my website to illustrate how useful math can be.

Here was the problem: Housekeepers working at her company have the option of bringing laundry home with them to do at their own convenience. Pretty cool, right? Except her pretty awesome company wants to make sure they compensate their employees for the price of doing said laundry at home. They figure that $.75/load for water, electricity, and detergent sounds fair, but they also want to account for the effect of each load on the longevity of the washing machine. I personally can't believe they would do this–and commend them for it–so let's take a look at how we can help:

**Assumptions**: a new laundry machine costs $600, can run for 7 years before repairs are needed, and might experience 300 loads/year. (read "/" as "per").

**Goal**: compensate employees for costs of repairs that might be incurred by the normal "wear and tear" each load of laundry performs on the machine.

So, we have just calculated that if we pay employees $0.29 per load, it would fairly compensate them for "wear and tear" on their machines. However, is this what we're really looking for? Do you see any issues with our assumptions?

Well, our calculations assume that a machine would be replaced after 2100 loads. In reality, if it breaks down, a repair for the machine would (hopefully) be less than $600. So what we have calculated is an "upper bound" for the amount to compensate employees. Let's say we round down to $0.25:

$525 is surely enough to cover any repairs that might need to be done. And now we have an idea of how to perform any other relevant calculations that we might be interested in. $0.15/load results in $315 for repairs, which also sounds like enough (though I've never dealt with a washing machine repairman).

And that's it. Hope you found this little walkthrough easy to follow. Until next time!