Questions on Word Problems: Problems on percentages, ratios, and fractions answered by real tutors!

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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.: 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(1756) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the fraction,
A/B
The first statement is,
1.(A+6)/(B-5)=3/4
Let's simplify this,
1.(A+6)/(B-5)=3/4
4(A+6)=3(B-5)
4A+24=3B-15
4A+24=3B-15
4A-3B=-39
From the second statement, the reciprocal of the original fraction is,
B/A
then,
2.B/A-1=16/9
From eq. 2,
2.B/A-1=16/9
B/A=16/9+9/9
B/A=25/9
9B=25A
You can substitute this value into eq. 1 and solve for A.
4A-3B=-39
Multiply both sides by 3,
3(4A-3B)=3(-39)
12A-9B=-117
Now substitute, 9B=25A,
12A-9B=-117
12A-25A=-117
-13A=-117
highlight(A=9)
You can then back substitute to find B.
9B=25A
9B=25(9)
highlight(B=25)
Check your answer.
Original fraction : 9/25
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First statement : (9+6)/(25-5)=15/20=3/4
First statement is true, so far so good.
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Second statement : 25/9-1=25/9-9/9=16/9
Second statement is true.
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Both are good answers.