The algebra teacher tonight decided to delay the test for another week. I'm on the fence as to whether this is a good thing or a bad thing. Oddly, for me, the most difficult material in the entire course is one the first test, being word problems in general and mixture and interest problems in specific.
Here's a mixture problem, from the text:
"A jeweler mixes 15g of a 60% silver alloy with 45g of a 20% silver alloy. What is the percent concentration of silver in the resulting alloy?"
Which I at first kept getting really funky and non-sensical answers for. And it turns out, as always, that the problem was one of the simplest arithmetic. Because, you know, 45 and 15 do not, in fact, equal 65. Once I realized that, it fell into place - like so:
Let X = the percentage of silver alloy in the final mix.
.6(15) + .2(45) = 60x
9 + 9 = 60x
18 = 60x
x = 18/60
x = .3 or 30%
30% was much better than the answer I was getting the first two times around with the 65g mix - 27.65%. Thankfully, the textbook authors know that the end users are likely to be idiots, so the correct answers are generally nice, round numbers, so my sloppy percentage was a tip-off that I'd fucked it up somewhere.
The issue I have with these problems is two-fold; I trip over my feet in my inability to abstract from language into math, and then that general unsureness tends to obscure whatever computational mistakes I make. Big car wreck, really.
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