One serious side effect of working in an educational shop is that many people who come into the shop assume that you are an expert. The honest truth is that I'm just a clerk. Yeah, I took math all the way up to calculus, but that was over a decade ago. Trying to dredge up how to set up certain equations is as difficult for me as it is for the people asking.
There was a question like that yesterday. A woman and her daughter came in. The daughter quickly vanished into the toys and games, but the mother handed me a sheet of the girl's homework and explained that she couldn't help her daughter with the problems. What she needed was a reference of some sort that would help her to figure out what to do when confronted with these problems. Well, we sell this great series of math handbooks, and I thought the best one would be Math on Call, a wonderful handbook organized by topic with reader-friendly descriptions of each... and it's at about the middle school level. So I confidently led her to the section with the books, pulled one off the shelf and handed it to her, and grabbed a copy of my own. Then we looked at the first problem on her daughter's worksheet. And I failed. Utterly failed. I couldn't solve the thing with the handbook.
I could, however, solve it without the help of the handbook. The problem was that I couldn't explain how I solved it in such a way that the mother could lead her daughter to solving it on her own. Here's (roughly) the problem:
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?
So, I solved it in my head, but I couldn't explain how well enough to help the mother. Other problems on the sheet were much easier, and I was able to demonstrate the usefulness of the handbook with those. But this problem was driving me nuts. Can you solve it?
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