How to solve an equation

I need help with this problem. I'm taking a College Algebra CLEP exam and my book does not very clearly explain answers..just goes here is your equation here is your answer...with no explanation...can someone help? Here is the question;

The difference between two positive integers is 15. The smaller number is 1/6 of the larger number. What is the value of the smaller number.

First it tells me that I should use x-y=15

we all know this is not possible without some type of craziness....so

It gives me y=(1/6)x

then just states that y is 3 and x is 18. How do they get this? Explain please!! :)

x-y = 15
x - 15 = y

y = x/6
x - 15 = x/6
6(x-15) = x
6x - 90 = x
6x - x = 90
5x = 90
x = 18

The approach they're taking seems to be … call the two numbers "x" and "y". Let "x" be the larger number.

"The difference between two positive integers is 15."
Therefore x - y = 15

"The smaller number is 1/6 of the larger number."
So 6y = x

Using substitution:
x - y = 15
6y - y = 15
5y = 15
y = 3

SOLUTION: The smaller number is 3.

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Check: The larger number = 6 * 3 = 18
The difference between 18 and 3 = 15

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My approach, which differs slightly from the one used above, would be to try to use as few pronumerals as possible right from the start.

The number we're looking for is "x".
It's one-sixth of another number; I'd call this other number "6x".

6x - x = 15
5x = 15
x = 3

The smaller number is 3. (The larger is 6*3 = 18; the difference = 15)

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Remember to answer the question!

"What is the value of the smaller number?"

Of course, to check, it's pretty much essential to find the value of the larger number too.

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