Question

Solve the following equations:
$\frac{x}{2}+\frac{y}{5}=5$.

$\frac{2}{x}+\frac{5}{y}=\frac{5}{6}$.

• A. $x=6;y=10$
• B. $x=5;y=6$
• C. $x=4;y=15$
• D. $x=3;y=9$

Answer 1

Answer: (A), (C)

The correct options are
A $x=6;y=10$
C $x=4;y=15$

Given equations are $\frac{x}{2}+\frac{y}{5}=5$ and $\frac{2}{x}+\frac{5}{y}=\frac{5}{6}$

Let $\frac{x}{2}=u$ and $\frac{y}{5}=v$

$u+v=5$ .....(i)

$\frac{1}{u}+\frac{1}{v}=\frac{5}{6}$ .....(ii)

$\Rightarrow \frac{u+v}{uv}=\frac{5}{6}\Rightarrow \frac{5}{uv}=\frac{5}{6}\Rightarrow uv=6$ .........(iii)

From (i) $v=5-u$

$(5-u)u=6\Rightarrow 5u-u^2=6\Rightarrow u^2-5u+6=0\Rightarrow u^2-2u-3u+6=0\Rightarrow u(u-2)-3(u-2)=0\Rightarrow (u-3)(u-2)=0\Rightarrow u=2,3$

But $\frac{x}{2}=u$

$\Rightarrow x=2u\Rightarrow x=4,6$

Also, $\frac{y}{5}=v$

$\Rightarrow y=5v\Rightarrow y=15,10$