SOLUTION: The denominator of a fraction is four more than the numerator. If both numerator and denominator are increased by six, the simplified result is 7/9. Find the original fraction.

Algebra ->  Rational-functions -> SOLUTION: The denominator of a fraction is four more than the numerator. If both numerator and denominator are increased by six, the simplified result is 7/9. Find the original fraction.       Log On


   

Question 1157037: The denominator of a fraction is four more than the numerator. If both numerator and denominator are increased by six, the simplified result is 7/9. Find the original fraction.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
Fraction, n%2F%28n%2B4%29

%28n%2B6%29%2F%28n%2B4%2B6%29=7%2F9
-
%28n%2B6%29%2F%28n%2B10%29=7%2F9
9%28n%2B6%29=7%28n%2B10%29
9n%2B54=7n%2B70
2n=70-54
n=35-27
n=8
-
The fraction, highlight%288%2F12%29



check------
%288%2B6%29%2F%2812%2B6%29=14%2F18=7%2F9

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numerator = +x+
The fraction is:
+x+%2F+%28+x%2B4+%29+
-------------------
given:
+%28+x+%2B+6+%29+%2F+%28+x+%2B+4+%2B+6+%29+=+7%2F9+
+%28+x+%2B+6+%29+%2F+%28+x+%2B+10+%29+=+7%2F9+
Multiply both sides by +9%2A%28+x+%2B+10+%29+
+9%2A%28+x+%2B+6+%29+=+7%2A%28+x+%2B+10+%29+
+9x+%2B+54+=+7x+%2B+70+
+2x+=+16+
+x+=+8+
and
+x+%2B+4+=+12+
--------------------
The fraction is +8+%2F+12+
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check:
+%28+x+%2B+6+%29+%2F+%28+x+%2B+10+%29+=+7%2F9+
+%28+8+%2B+6+%29+%2F+%28+8+%2B+10+%29+=+7%2F9+
+14+%2F+18+=+7%2F9+
+%28+2%2F2+%29%2A%28+7%2F9+%29+=+7%2F9+
+7%2F9+=+7%2F9+
OK