The denominator of a fraction is …
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Sia ? 6 years, 7 months ago
Let the numerator and denominator of the fraction be x and y respectively.
Then,
Fraction= {tex} \frac { x } { y }{/tex}
It is given that
Denominator = 2 (Numerator) + 4
{tex}\Rightarrow{/tex} {tex}y = 2x + 4 {/tex}
{tex}\Rightarrow{/tex}{tex}2x - y + 4 =0{/tex}
According to the given condition, we have
{tex}y - 6 = 12(x - 6){/tex}
{tex}\Rightarrow{/tex} {tex}y - 6 =12x -72{/tex}
{tex}\Rightarrow{/tex} {tex}12x - y - 66 =0{/tex}
Thus, we have the following system of equations
2x - y + 4 =0 ............(i)
12x - y -66 =0 .............(ii)
Subtracting equation (i) from equation (ii), we get
10x - 70 =0 {tex}\Rightarrow{/tex} x = 7
Putting x = 7 in equation (i), we get
14 - y + 4 =0 {tex}\Rightarrow{/tex} y = 18
Hence, required fraction ={tex}\frac { 7 } { 18 }.{/tex}
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