Wow. I expected very little or no response to that math problem I posted. I'm a little surprised at how many of you decided to take a shot at it. Here's the problem once more:
During a basketball game, Jen makes 60% of her free throws. Donna makes 75% of her free throws. If, together, they made twelve free throws out of eighteen attempts, how many free throws did each woman attempt?
As I mentioned, I was standing with a customer trying vainly to explain how a handbook could help her solve this problem. I sort of blanked out for a moment as I tried to visualize how to solve the problem. For me, there were some important facts stated in the problem. The numbers are free throws, which means they are whole numbers, no fractions or decimals. Because they are free throws and not normal baskets, they could be even or odd. There were six misses... and those misses made up 25% of one set and 40% of another. And that's how I attacked the problem. I first assumed that each woman had missed three and told myself, "If Donna missed three, then she attempted twelve. Which leaves six for Jen, but three is half of six, so that's not right." So I plugged in two for Donna. "If Donna missed two, she attempted eight, which leaves ten for Jen, and that four left over is forty percent of ten, which means that I have the right answer." I then attempted to explain my method to the poor mother, who understood well enough, but like me couldn't figure out how to teach that to her daughter.
Although I came up with the answer fairly quickly, if a professor wanted me to write it down I would be in loads of trouble. So later that night, before sleeping, I posed the question (complete with my confused answer) to hubby-Eric, who first came up with a set of equations with four variables, then two. His explanation made perfect sense to me, and reminded me how to solve that type of problem. I can now confidently explain it to the next person who happens to hand me that sort of thing (and thanks to Rich I've got an even more elegant example of how to set up the equation if that poor mother wanders in again).
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