SOLUTION: the denominator of a rational number is 2 more than its numerator.if numerator is increased 4 times,and 8 is added to tge denominator l.the new number would be 4/3.find the orginal

Algebra ->  Equations -> SOLUTION: the denominator of a rational number is 2 more than its numerator.if numerator is increased 4 times,and 8 is added to tge denominator l.the new number would be 4/3.find the orginal      Log On


   

Question 1087819: the denominator of a rational number is 2 more than its numerator.if numerator is increased 4 times,and 8 is added to tge denominator l.the new number would be 4/3.find the orginal number solution
Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numerator = x
So the denominator = x+2
So the fraction = x%2F%28x%2B2%29 .... ...... ..... (1)
As per the condition,
%28x%2A4%29%2F%28x%2B2%2B8%29+=+4%2F3
+4x%2F%28x%2B10%29+=+4%2F3
By cross-multiplying the equation,
12x++=+4%2A%28x%2B10%29
12x+=+4x%2B40
Subtracting 4x both the sides,
12x-4x+=+4x-4x%2B40
8x+=+40
x+=+40%2F8+=+5%3B++x+=+5
Replacing the value of x in (1),
x%2F%28x%2B2%29+=+5%2F7
The original rational number = 5%2F7. Answer.
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