Solving a Math Poem
Date: 05/24/2000 at 14:04:06 From: Amber Subject: Math poem Take five times which plus half of what And make the square of what you've got. Divide by one and thirty square To get just four - that's right, it's there. Now two more points I must impress: Both of which and what are fractionless, And what less which is not a lot: Just two or three. So now, what's what? My teacher gave me this problem to try and figure out but every time I look at it, it doesn't make sense. I get stuck at the beginning. Please help me! Thank-you very much for your time and effort, Amber
Date: 05/25/2000 at 11:24:01 From: Doctor TWE Subject: Re: Math poem Hi Amber - thanks for writing to Dr. Math. When I get a problem like this, the first thing I do is read it over several times, trying to understand a little bit more of it each time. (I had to read this one over three times before I understood what it was asking, and then I had to reread parts of it again as I worked it out!) To solve this, you need to realize that 'what' and 'where' are numbers, which we'll represent with variables. I'll use X = what and Y = where. Now it helps to write the word problem (poem) in the form of an algebraic equation. The problem is that English - especially when used poetically - is not as precise as algebra, so some parts are open to multiple interpretations. I'll get you started: "Take five times which plus half of what," This is easy; algebraically it's: 5*Y + (1/2)X "...and make the square of what you've got." Here we have to decide if the word 'what' means the variable X or is just part of the expression "what you've got." If we interpret the "and make the square of what" as X^2, the "you've got" doesn't make any sense. So I interpret this as meaning take the square of the expression so far. That's: [5*Y + (1/2)X]^2 "Divide by one and thirty square," Again, this is not clear. This could mean divide by 31^2 = 961, or it could mean divide by 1 + 30^2 = 901. I'll leave it to you to figure out which interpretation is correct (only one works). Now we have either: [5*Y + (1/2)X]^2 / (31^2) or [5*Y + (1/2)X]^2 / (1+30^2) "...to get just four-that's right, it's there." This completes the equation. We have either: [5*Y + (1/2)X]^2 / (31^2) = 4 or [5*Y + (1/2)X]^2 / (1+30^2) = 4 "... both of which and what are fractionless," This means that X and Y are integers. This is useful information, especially if you have to resort to trial-and-error, since you only have to try integer combinations. "...and what less which is not a lot: just two or three." This translates to: X - Y = 2 or 3. This gives us four possible combinations to try: [5*Y+(1/2)X]^2 / (31^2) = 4 and X - Y = 2 [5*Y+(1/2)X]^2 / (31^2) = 4 and X - Y = 3 [5*Y+(1/2)X]^2 / (1+30^2) = 4 and X - Y = 2 [5*Y+(1/2)X]^2 / (1+30^2) = 4 and X - Y = 3 "So now, what's what?" This tells us that they're looking for the value of X. Can you take it from there? I hope this helps. If you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/
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