Question 151029
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.