Translating Words into Math
Date: 8 Mar 1995 22:51:36 -0500 From: Anonymous Subject: Algebra. Dear Dr. Math, I need help with my Algebra. We are doing story problems. I DON'T want you to do them for me. I just need help on understanding them so that I can solve them by myself. I am stuck on one particular problem. The number is decreased by 1/3 of the number. The result is 62. Find the number. Please help me. Brittany I
Date: Thu, 09 Mar 1995 12:57:09 +0000 From: Dr. Math Subject: Re: Algebra. Hello there! I think the hardest thing about doing these problems is translating sentences into mathematical equations. Basically, you have to pick them apart, piece by piece, translating one part at a time until what you have left is an equation that you can solve using Algebra. So let's dig in. Actually, I'll make up a new problem that's similar to yours, and I'll lead you through the translation process on that one. Here it is: A number is increased by 3/4 of the number, and the result is 28. What is the number? One of the first things we want to do is to replace "the number" by a variable. You can call it anything you want, and in this case I'll call it x. So we go through the sentence and wherever we see the phrase "the number" or "itself" or something that obviously refers to the number we're talking about, we replace that by an x. So we get: x is increased by 3/4 of x, and the result is 28. What is x? Also, one of the first things you want to do in these sentences is find out where the equal sign goes. Typically, you'll look for the verb "is," or "the result is," or if they're really throwing it out at your face, "is equal to." In our problem, we find our equal sign in "and the result is": x increased by 3/4 of x = 28. (I changed the grammar just a teency bit) Now what does 3/4 of x mean? It means we multiply 3/4 times x. So now we have x increased by 3/4 * x = 28. Now there's only one thing left. We need to figure out what "increased by" means. What would I mean if we were baking cookies, and I said to you "increase the amount of chocolate chips by two cups"? I'd mean that you would add two extra cups of chocolate chips to the batter, i.e. ADD two cups, and we'd both have a stomach ache. So the phrase "increased by" is probably going to mean "plus." x + 3/4 * x = 28. And now we have a bona fide Algebraic sentence. Notice the period at the end. Usually people don't write those, but I wanted to show you that even when we write down something as weird as "x + 3/4 x = 28", it can always be read as a real English sentence, with punctuation at the end and everything. So see if you can apply the same techniques to solve your problem. If you still have trouble, write back! -Ken "Dr." Math
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