“Spacely Sprockets sells its widgets through a preferred buyer program. Buyers get a 1% discount off of the base price for each thousand sprockets they bought in the previous calendar year. If Ricky’s Rockets ordered 18,000 sprockets last year, and the base price per sprocket is $1.25, how much will Ricky spend on sprockets if he uses 50% more sprockets than he did during the previous year?”
First of all, if you look at that and see a jumble of words and start to panic. Don’t! We can turn this word problem into a manageable equation or set of equations if we carefully walk through it step by step.
Second, the way that you go about doing that can make the difference between an easy solve and a more challenging one. Here’s how many people would start…
“So Ricky uses x sprockets at a price of y for a total cost of z.”
What magical power does x have? Who came along and said, “When we teach children algebra, the first variable we give them must be x”? The answer, sadly, is probably that x was chosen because it was good for so little else. If we want a completely nondescript variable that isn’t likely to be confused with anything else, x is a good choice. Unfortunately, very few of the problems that we face are algebra for algebra’s sake where using generic variables makes sense. Take this problem for example.
We need to figure out the quantity and the price to figure out the total cost. So here’s a crazy idea:
Why not use variables that make sense?
q=18,000*150%/100 = 24,000
When you use variables that actually relate to the pieces of the problem, it’s going to make more sense how they fit together. Plus, you’re less likely to get them mixed up when you have an idea of what each variable means!
Don’t just throw an x in for an unknown because it’s x and it has some kind of magical powers. Use variables that make sense in your word problems, and be amazed at how it reduces the number of silly mistakes that you make.