SOLUTION: The denominator of a rational number is 9 less than three times the numerator. The number in simplest form is 3/8. Find the number

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Question 28256: The denominator of a rational number is 9 less than three times the numerator. The number in simplest form is 3/8. Find the number
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Let the fraction be x%2Fy.

We know that y = 3x-9

We also know that x%2Fy+=+3%2F8, or 8x = 3y

So we have 2 equations:
3y=8x
y = 3x-9 --> multiply this by 3, to scale it up:

3y=8x
3y=9x-27

Subtracting the 2 equations gives us
0 = -x+27
so x=27

since x/y is of form 3/8 and we know that x is actually 27, we need to scale the 3 upto 27 (ie multiply by 9), so the 8 needs to be 8*9 --> 72

The fraction is 27/72.

CHECK: 27*3 = 81
and 81 less 9 is 72... correct.

jon.