SOLUTION: The numerator of a fraction is 7 less than the denominator.If one and one third is added to it,the fraction obtained is 14/9.Find the original fraction?

Algebra ->  Finance -> SOLUTION: The numerator of a fraction is 7 less than the denominator.If one and one third is added to it,the fraction obtained is 14/9.Find the original fraction?      Log On


   

Question 1119507: The numerator of a fraction is 7 less than the denominator.If one and one third is added to it,the fraction obtained is 14/9.Find the original fraction?
Found 2 solutions by htmentor, josmiceli:
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
(x-7)/x + 4/3 = 14/9
Multiply through by x and simplify:
x - 7 + (4/3)x = (14/9)x
x + (12/9)x - (14/9)x = 7
(7/9)x = 7
x = 9
Thus the original fractions is 2/9

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the denominator
The original fraction is:
+%28+x+-+7+%29%2Fx+
------------------
+%28+x+-+7+%29+%2F+x+%2B+1+%2B+1%2F3+=+14%2F9+
Convert constants on the left side to ninths
+%28+x+-+7+%29%2Fx+%2B+9%2F9+%2B+3%2F9+=+14%2F9+
Multiply both sides by +9+
+%28+9%2A%28+x+-+7+%29+%29%2Fx+%2B+9+%2B+3+=+14+
+%28+9x+-+63+%29%2Fx+%2B+12+=+14+
+%28+9x+-+63+%29+%2F+x+=+2+
+9x+-+63+=+2x+
+7x+=+63+
+x+=+9+
---------------------
+%28+x+-+7+%29%2Fx+=+%28+9+-+7+%29+%2F+9+
+%28+x+-+7+%29%2Fx+=+2%2F9+
--------------------------------
check:
+2%2F9+%2B+1+%2B+1%2F3+=+14%2F9+
Multiply both sides by 9
+2+%2B+9+%2B+3+=+14+
+14+=+14+
OK