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

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) (Show Source): You can put this solution on YOUR website!
Here's the fraction,

The first statement is,
1.
Let's simplify this,
1.

From the second statement, the reciprocal of the original fraction is,

then,
2.
From eq. 2,
2.

You can substitute this value into eq. 1 and solve for A.

Multiply both sides by 3,

Now substitute, ,

You can then back substitute to find B.

Check your answer.
Original fraction :
.
.
.
First statement :
First statement is true, so far so good.
.
.
.
Second statement :
Second statement is true.
.
.
.
Both are good answers.

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