I always recommend that students write out (in sentence form) what the equations are (shoving in Xs).
So:
Wins + Loses = Total Games
2x + X = 36
That way, you'd see that you were missing the X representing loses.
Also, I find it easier to use a letter than has some meaning (rather than an X). So, I'd use L (for loses), just to remind me what I was using as my reference (so at the end, I wouldn't think that X represented the wins).
But in order to solve the problem you need to be able to write the one equation (house 1 plus house 2 = 4400 sq feet), you can only have one variable. Therefore, you need to describe one of the variable in terms of the other.
So:
House 1 = X
House 2 = 2X-1000
OR
House 2=X
House 1=0.5(X+1000)
Choose which ever one is easier (i.e. option 1, which doesn't have a fraction).
There is no way to solve the equation if you have:
X+Y=4400 (where X is house 1 and Y is house 2).
Well, I do work as a teaching assistant, but it is epidemiology and biostatistics to graduate students. Come to think of it though, I still tell them to write things out. And I still do it myself.
But in order to solve the problem you need to be able to write the one equation (house 1 plus house 2 = 4400 sq feet), you can only have one variable. Therefore, you need to describe one of the variable in terms of the other.
So:
House 1 = X
House 2 = 2X-1000
OR
House 2=X
House 1=0.5(X+1000)
Choose which ever one is easier (i.e. option 1, which doesn't have a fraction).
There is no way to solve the equation if you have:
X+Y=4400 (where X is house 1 and Y is house 2).
I didn't see your post when I posted my way of working it out. I think I see it now...I'm gonna work the problem out on my own again & see if I can think thru the language - why they are set up this way.
And then find some more problems....MAYBE I can get it in one night!
No, don't think that, or it will come true! You are making this more complicated than it is.
In all of the problems you posted, there is one value that all the others are related to. Wiley's score was more or less than the other students' scores, the games won were more than the games lost. They relate to each other.
That item that the others relate to is your single variable. You can call it X or use the suggestion of the first letter of what it represents. W for Wiley's score, or L for games lost.
Then you assign value to the other things by how they relate to the variable.
Games won is twice L; that means 2L. Greg's score is Wiley's score - 6, so W-6.
Then you can line them all up and solve for the unknown.
There are examples where you'd have two variables, but then you'd also have two totals. These are more complex though.
Don't give up about your test. You are so close to getting it. You had everything set up correctly, you just did think to sub-in for S and (using the equations you had already figured out). One wee little step further and you'd have had it.
You will get to those type problems...but don't worry about that tonight!!
Try this strategy:
Read the word problem. Don't try to figure anything out yet. Then read it again. See if you notice which thing is the one that the others relate to. If not, try writing it down, like you did with the test score problem. You had the right set-up with W, W -6 and W+10. Then all you have to do is add them together and solve for your unknown.
Thanks for the help guys! I'm gonna get to studying some more math & then some of the other subjects & get to bed in a bit - I have to be there @ 7:30 a.m. & its about a 45 min drive from here! UGH!
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