SOLUTION: The denominator of a certain fraction is six times the numerator. If 3 is added to the numerator and subtracted from the denominator, the resulting fraction is equivalent to 2/5. F

Question 527396: The denominator of a certain fraction is six times the numerator. If 3 is added to the numerator and subtracted from the denominator, the resulting fraction is equivalent to 2/5. Find the original fraction.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Define the original fraction as:
.
x/6x
.
Adding 3 to the numerator and the denominator:
.
(x+3)/(6x+3) = 2/5
.
Cross multiply:
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(x+3) * 5 = (6x+3)*2
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5x +15 = 12x +6
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-7x = -9
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x = 9/7
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Check the answer:
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6x = 54/7
x/6x = (9/7) / (54/7) = 9/7 * 7/54 = 9/54 = 1/6
That's the correct ratio.
.
9/7+3 = 9/7 + 21/7 = 30/7
6x+3 = 6*9/7 + 21/7 = 54+21 /7= 75/7
(x+3)/(6x+3) = (30/7) / (75/7) = 30/7 * 7/75 = 30/75 = 2/5
Correct.
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Answer: The original fraction is 9/7.
.
Done.
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