SOLUTION: please help me solve this, its a word problem so I don't have an exact equation quite yet. The denominator of a fraction is four more than three times the numerator. If both numera

Algebra ->  Rational-functions -> SOLUTION: please help me solve this, its a word problem so I don't have an exact equation quite yet. The denominator of a fraction is four more than three times the numerator. If both numera      Log On


   

Question 1100798: please help me solve this, its a word problem so I don't have an exact equation quite yet. The denominator of a fraction is four more than three times the numerator. If both numerator and denominator are decreased by seven, the simplified result is 2/15. Find the original fraction. (Do NOT simplify.)


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = original numerator
Let +b+ = original denominator
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given:
(1) +b+=+3a+%2B+4+
(2) +%28+a+-+7+%29+%2F+%28+b+-+7+%29+=+2%2F15+
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(1) +-3a+%2B+b+=+4+
Multiply both sides of (2) by +15%2A%28+b+-+7+%29+
(2) +15%2A%28+a+-+7+%29+=+2%2A%28+b+-+7+%29+
(2) +15a+-+105+=+2b+-+14+
(2) +15a+-+2b+=+91+
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Multiply both sides of (1) by +2+
and add the equations
(2) +15a+-+2b+=+91+
(1) +-6a+%2B+2b+=+8+
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+9a+=+99+
+a+=+11+
and
(1) +b+=+3a+%2B+4+
(1) +b+=+3%2A11+%2B+4+
(1) +b+=+37+
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The original fraction is 11/37
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check:
(2) +%28+a+-+7+%29+%2F+%28+b+-+7+%29+=+2%2F15+
(2) +%28+11+-+7+%29+%2F+%28+37+-+7+%29+=+2%2F15+
(2) +4%2F30+=+2%2F15+
(2) +2%2F15+=+2%2F15+
OK