SOLUTION: The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by three, the simplified result is 19/20. Find the original fraction.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by three, the simplified result is 19/20. Find the original fraction.       Log On


   

Question 1157906: The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by three, the simplified result is 19/20. Find the original fraction. (Do NOT simplify.)
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numerator be +n+
given:
The fraction is +n+%2F+%28+n+%2B+2+%29+
+%28+n+%2B+3+%29+%2F+%28+n+%2B+5+%29+=+19%2F20+
Multiply both sides by +20%2A%28+n+%2B+5+%29+
+20%2A%28+n+%2B+3+%29+=+19%2A%28+n+%2B+5+%29+
+20n+%2B+60+=+19n+%2B+95+
+n+=+35+
and
+n+%2B+2+=+37+
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The original fraction was 35/37
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check:
+%28+n+%2B+3+%29+%2F+%28+n+%2B+5+%29+=+19%2F20+
+%28+35+%2B+3+%29+%2F+%28+40+%29+=+19%2F20+
+38+%2F+40+=+19+%2F+20+
+19+%2F+20+=+19+%2F+20+
OK
check my math

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


The same number was added to both numerator and denominator, so in the new number the denominator is STILL 2 more than the numerator.

So rewrite the simplified fraction 19/20 as an equivalent fraction in which the denominator is 2 more than the numerator: 38/40.

Now subtract the 3 that were added from numerator and denominator to get the original fraction, 35/37.