Only difficulties with a part of a simple question

[Chris8080]

Hi,

the question:
What is the ratio of y to x?
(1) y = 3x
(2) x = 11
very obviously until here. I got it right. But finally the explaination confuses me:

(1) y in terms of x. Substituting for y in the rephrased question, we get y / x = 3x / x = 3. The ratio of y to x is 3.
(2) y / x = y / 11. The ratio of y to x is y / 11

The term y / x, that's clear. But 3x / x ... this is what I don't undestand.
y / x = 3x / x => y / x = 3 => y = 3X allright - I got it.
Can you help with the 3x/x .. where does it come from?

Thank you in advace.
Bye, Chris

[Svedankae]

hey bud they just divided both sides by "x".... thats everything

[Chris8080]

Yes .. that's clear. Sorry .. I think my point wasn't.

How to get the idea to do this?
I just saw y = 3x .. is a ratio, so y to x is solveable with this.
Is there a rule for an approach like:
Everytime one sees ratio x to y and an answer mx = ny devide it by either m or n or something like this?

Sorry, it's hard to describe. Sometimes I have a lack of an understanding for some of the steps to take .. or even better: How to get the right ideas.

I guess what I'm lacking of is this sentence:
The ratio of y to x can be expressed as a fraction, so the rephrased question is “what is y / x?”
So .. I first have to state this before I know what to do.
But on the other hand, I was able to figure out the right solution just by looking at the answer.

[Osirus@VeritasPrep]

hey Chris,

its basically just algebra. If you're looking for y/x when you take the first statement (y = 3x) you have to essentially solve for y/x. In order to solve for y/x you need to divide both sides by x. You would end up with y/x=3/1. That's the ratio. The ratio is 3:1 so we know that statement one alone is sufficient. Using the same logic as before, statement 2 alone only gives us y/11 which still doesn't tell us what y is so statement two is insufficient.

I think the key is to look at the equation and think about how to solve for the variable algebraically, but with ratios instead of solving for x or y, you were solving for the ratio; in this case y/x. So you want to manipulate the equation to get y/x on one side of the equation if that is possible then you know just determined the ratio. Hope that was clear and helpful.

[Svedankae]

But on the other hand, I was able to figure out the right solution just by looking at the answer.

and that is perfectly fine. dont worry about this, i would have come to the same conclusion as you just by looking at it... the explanations to these problems are for people for whom these things are not obvious.

[Chris8080]

Hope that was clear and helpful.

Of course it was.
Thank you very much!

@Svedankae: Ok .. but after having a real bad test result, I want to make sure that my brain gets more mathmatical