## Some Practical, (Extremely) Simple Algebra

Early in secondary school, many of my classmates used to be exasperated by the perceived lack of practical application of the mathematics we had to learn at the time. I never really understood why, because it had clear practical applications, though I admit I also simply thought it was fun. Later on, things like statistics were really boring, but I figured I’d share how the simplest of elementary algebra can help you make financial choices.

Having just moved, we had to decide whether or not to buy a washing machine. Washing machines start at about €400 — they can be obtained used for much less, but last time I picked up a used washing machine for €40 it broke within about a year and it’s just so much trouble trying to fix it or getting yet another used replacement — while laundromats cost about €3-4 per load (+20 cents for detergent). Admittedly the load sizes are slightly larger at the laundromat, but I don’t see that as a good thing: it just makes it harder to carry and dry the laundry.

Washing costs per load for various temperatures in € according to Nibud
temperature/ type of costs 90°C 60°C 40°C
electricity 0.48 0.25 0.15
water 0.10 0.08 0.08
washing powder 0.19 0.19 0.19
depreciation / maintenance 0.48 0.48 0.48
total 1.25 1.00 0.90
total without depreciation 0.77 0.52 0.42

We usually wash on 30 degrees and have an otherwise energy and water efficient washing machine, but I’ll just run with the price for a single wash without depreciation value. I’m not interested in depreciation of the value of the washing machine, since the point is how many times you have to wash to break even compared to the laundromat. Of course a depreciation value could be used for this so that ax = bx should yield a useful conclusion, but that’d be a bit of a roundabout way.

I devised the following simple formula: ax = bx + c, where a is the cost of one load at the laundromat, b is the cost of one load in a self-owned washing machine, and c is the price of a washing machine. x is the break even point of the number of washes required to make it worth your while to buy a washing machine as opposed to utilizing a laundromat.

```3.20x = .42x+480 (-.42x)
2.78x = 480
x=480/2.78=173```

I haven’t counted the number of times we’ve washed, but if we haven’t surpassed it yet, I bet we’re quite close. We’ve had it for nearly two years and we wash slightly more than once a week on average.