OG 12. PS#106, alternate solution?

[jeremy8]

[spoiler]When positive integer "x" is divided by positive integer "y", the remainder is 9. If x/y = 96.12, what iis the value of "y".

A.96
B.75
C.48
D.25
E.12[/spoiler]
The way I solved this question was by isolating the decimal, so:

0.12 = 3/25

Since the remainder is 9, I just mutliplied the numerator (effectively the remainder) and denominator in 3/25 by 3 = 9/75, and found "y" to be 75.

Does this sound reasonable? Their method seems like it would take forever under exam conditions.

[mj78ind]

May I know what is the question.......

[jeremy8]

May I know what is the question.......

Sorry, fixed it in my original post. I was kind of worried about copyright issues I keep reading about concerning the OG, but maybe it only applies to commercialization.
If not, no copyright infringement intended!

Put it under a spoiler, just in case. Not that it really changes anything, but...

[mj78ind]

Got it

x = 96Y + 0.12Y;

Now 0.12Y should equal 9, 0.12Y = 9 gives, y = 75.

Hence you are right about the answer, but may be the methodology could be revised slightly

[sars72]

remainder is 9

so, 9/y = 0.12

-> y = 9/0.12 = 75

[jeremy8]

Thanks for the answers.

I should've been more specific in my post. I know how to get the solution using algebra, I was just wondering about the legitimacy of using the method I used, which is faster than 9/.12, since it simply requires treating 3/25 like a ratio and multiplying both numerator and denominator by 3 to find that y=75.

However, I wasn't sure whether this is a sound technique or whether I got to the right answer by luck, but this wouldn't work in a different context.