SOLUTION: if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. if the reciprocal of the original fraction i

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. if the reciprocal of the original fraction i      Log On


   

Question 151029: if the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. if the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. find the original fraction.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the fraction,
A%2FB
The first statement is,
1.%28A%2B6%29%2F%28B-5%29=3%2F4
Let's simplify this,
1.%28A%2B6%29%2F%28B-5%29=3%2F4
4%28A%2B6%29=3%28B-5%29
4A%2B24=3B-15
4A%2B24=3B-15
4A-3B=-39
From the second statement, the reciprocal of the original fraction is,
B%2FA
then,
2.B%2FA-1=16%2F9
From eq. 2,
2.B%2FA-1=16%2F9
B%2FA=16%2F9%2B9%2F9
B%2FA=25%2F9
9B=25A
You can substitute this value into eq. 1 and solve for A.
4A-3B=-39
Multiply both sides by 3,
3%284A-3B%29=3%28-39%29
12A-9B=-117
Now substitute, 9B=25A,
12A-9B=-117
12A-25A=-117
-13A=-117
highlight%28A=9%29
You can then back substitute to find B.
9B=25A
9B=25%289%29
highlight%28B=25%29
Check your answer.
Original fraction : 9%2F25
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First statement : %289%2B6%29%2F%2825-5%29=15%2F20=3%2F4
First statement is true, so far so good.
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Second statement : 25%2F9-1=25%2F9-9%2F9=16%2F9
Second statement is true.
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Both are good answers.