Easy Proportion, but not for me

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The discussion centers around solving a word problem involving interest rates and principal amounts. One participant initially presents a solution using proportions but later discovers a simpler method using a single equation. The equation .03*x + .05*(6000-x) = 220 is highlighted as an effective approach. The conversation emphasizes the importance of understanding the relationship between principal, rate, and interest, suggesting that practice improves problem-solving skills. Ultimately, the focus is on finding the most efficient method to tackle such problems.
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EDIT: Problem Solved please delete.
 
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There's a much easier way to do it with one equation and no proportions. Practice makes word problems easier!

.03*x+.05*(6000-x)=220
 
Dr. Lady said:
There's a much easier way to do it with one equation and no proportions. Practice makes word problems easier!

.03*x+.05*(6000-x)=220

Actually that looks more complicated to me. My way was right too though, right?
 
Sure... but you can't always rely on guess and check. In this problem we see that there's a principal, a rate, and an interest. We need a problem that accomadates them and only them, and we happen to have P*r=I, which we just need to modify for our uses. Word problems are almost always best thought of as what variables you have and need, and then what equation you already know that relates them.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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