Translating word problems into Systems of equations.

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kreeto

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Hello everyone!
I started telling people at my school about this website (which I think is gold!!). Anywho! I am having trouble deciphering what exactly the 2 equations are from this word problem.
"The length of a piece of sheet metal is twice the width. The difference in length and width is 20in. What are the dimensions?"

So far I have the first equation as W-L=20 and I am thinking the 2nd equation is L=2W. It just does not make any sense to me. Is that right? I really just need help on the 2 different equations.
 
You almost have it but need to think a bit more. If L=2W, then which is larger, L or W (of course L and W are both positive)????

After answering my question, do you think that W-L=20 can be correct (If W-L =20, then which is larger, L or W?)
 
Always define your variables first, ie
Let W = width in inches and L be length in inches.

Now "the length is twice the width" translates as L = 2W. (So you have this correct. I'm interested to know WHY that doesn't that make sense to you?)

By implication this means that L is larger than W.

So "the difference in length and width" translates as L - W = 20 (You have this equation the wrong way around.)
 
The length of a piece of sheet metal is twice the width.
Let L= The length of a piece of sheet metal
Let W = the width
is means =
So The length of a piece of sheet metal is twice the width becomes L = 2*w
 
oh my goodness I have no idea why I kept getting hung up right there now that I did it right, it makes so much sense. I guess I am just too tired to see it through. I need to SLEEP!!!
 
I have L-W=20 and L=2W. Using substitution I got (2W)-W=20 which simplifies to W=20. And then of course by plugging that into L-(20)=20, L=40. I guess sometimes you need a little outside perspective.
 
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