Word Problems Frustration Linger

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I want to think the way math people think when it comes to word problems. I understand that I should ALWAYS let x represent what I am looking for, right? I can also let ANY letter represent what I am looking for. My problem comes when TRYING to create the right equations to help my plug and chuck away the word problems. I am so frustrated. Here I am ready to take calculus 1 this coming fall and word problems(ANY GRADE LEVEL) are killing me.

Here it a perfect example:

Bill invested a sum of money at 9% and a second sum at 18%. The second sum was $450 less than the first. He received a yearly amount return of $162 from his investments. How much was placed at 18%?

The book set up this equation:

.09x + .18(x - $450) = $162.

Of course, I can solve for x and then subtract $450 from whatever x is but my ETERNAL question is: HOW DO I LEARN TO SET UP EQUATIONS FROM WORD PROBLEMS? Also, can ALL students taking calculus 1 set up equations from word problems? I just don't want to be too deep over my head. Okay?

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In this case I'd use two variables (x and y)

X is invested at 9% and y at 18%
the amount at 18% was $450 less than the amount at x. From both accounts he received $162

so I got two equations in two unknowns
x-y=450 or y=x-450
0.9x+0.18y=162

you can either use substitution (like you're alluding to) or elimination to solve for x & y.

elimination
-x+y=-450
x+2y=16200/9
3y=16200/9-450
&
y=1/3(16200/9-450)
x=459+1/3(16200/9-450)

Setting up word problems is what math is all about. The skills follow the logic. Also a good basis in algebra is required for calculus. So I'd say most should be able to, whether they can is another matter.

Rap c∫ Confused

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ok
I thank you for your input.

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Word Problems Frustration Linger

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