The August 31 meeting saw a minor debate about the value of algebra in everyday life. Although a couple of the geeks claimed that they actually use algebra once in a while, nobody could come up with a concrete example on the spot. It was a pretty dismal performance on the part of said geeks, to say the least.In order to partially rectify (now that's a funny word!) the situation, here's a real problem from the real life of a real geek:
A geek wants to put four drawers one on top of the other into his workbench. He wants to make each drawer 15% taller than the one above it. The total available vertical space is 27 inches. How tall should he make each of the four drawers?
One way to solve this problem involves basic algebra. Are there other ways that don't? Please comment if you have one.
It depends upon what you call Algebra. After helping Phyllis flounder about a bit, I decided to see if I could think of the way my algebra-free father might have done it. Here is what I think he might have done:
ReplyDeleteAssume for a moment that the top most shelf is 1 inch high, the next is 1.15 inches, the next is then 1.15*1.15 inches =>1.3225), the bottom one is 1.520875 inches. Adding all these up, we get a total of 4.993375 inches. This means that the top shelf must actually be 27/4.993375 or 5.40716449 inches. This is, of course, completely equivalent to the solution of the equation:
x + x * 1.15 + x * 1.15^2 + x * 1.15^3 = 27.
Actually, as I think about it, I suspect my father might not have immediately hit upon the idea of assuming that the top shelf is 1 inch. He more likely would have guessed some height for the top shelf, say 5 inches, computed the total, divided it into 27 and then scaled the initial guess accordingly.
A way for the visually oriented person to think about it (actually the way I explained it to Phyllis): Imagine drawing a picture of the stack-up on a rubber band with the "top shelf" set to 1 inch high, stretching the rubber band until the "total height" equals 27 inches, then measuring the resulting height of the drawn top shelf.
The major advantage of the algebraic solution is that it provides a virtually automatic way of getting the solution. The other ways require some actual thinking.
That's the same algebra-free solution I came up with. Assume a height for the top drawer, calculate the total for all four, then scale the results as needed to get the 27 inches.
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