How Do You Figure Out the Equations for Word Problems?
Date: 04/09/2006 at 19:58:07 From: Marissa Subject: How do you make equations out of any word problems? I am so messed up with word problems. I can solve the equations, I just can't set them up correctly. If someone gives me the right equations I can do it. For example: Mrs Johnson is five times as old as her son. Three years ago she was eight times as old as her son then. Find each of their ages. I put 5s(-3 + 8s), but I'm soooo confused. Please help!
Date: 04/09/2006 at 23:13:12 From: Doctor Peterson Subject: Re: How do you make equations out of any word problems? Hi, Marissa. A lot of students have trouble with this; I see them all the time even at the college level. What you're having trouble with is translating from English into algebra, and I think it helps a lot to actually think of it as translating from one language to another. To do that, you start with a "dictionary". We first need to define a variable; you seem to have done that, but it's helpful to state your definition clearly: Age of son = s Now, we have other phrases or quantities in the problem, and we can write an expression for each phrase, gradually building up to a full equation. First, how old is Mrs. Johnson? Mrs. Johnson is five times as old as her son means Age of Mrs. Johnson = 5s Now we come to the big, complicated sentence: Three years ago she was eight times as old as her son then. We can break this down into several parts; I'll rewrite it with an emphasis on the numbers involved: her age 3 years ago = eight times her son's age 3 years ago Now, we need to add these phrases to our dictionary: her age 3 years ago = her son's age 3 years ago = eight times her son's age 3 years ago = Can you start to see how to fill these in? Three years ago, both of them were 3 years younger, which means we subtract 3 from their current ages. Then we can multiply by 8: her age 3 years ago = 5s - 3 her son's age 3 years ago = s - 3 eight times her son's age 3 years ago = 8(s - 3) Now, the sentence just says that two of these quantities are equal: 5s - 3 = 8(s - 3) With experience, you can write an equation like this directly, but at first it will be a good idea to take it very slowly and build it up piece by piece this way. I like to look at the overall meaning of a sentence first (which is what a language translator does--he doesn't just translate one word at a time, because different languages have different word order). By rewording the sentence to make its meaning clearer, I was able to change it into algebra more easily. But still I had to take my time! If you have any further questions, feel free to write back. I'd like to hear whether this helps, and perhaps see you try another example. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.