Question

If $\frac{10-3x}{5+2x}=\frac{m}{n}$ ; make $x$ as the subject of formula. Hence, find the value of $x$, if $3m-4n=2$ and $n=2.5$.

• A. $x=\frac{5(2n-m)}{2m+3n}$ and $x=\frac{10}{31}$
• B. $x=\frac{2(2n-m)}{7m+9n}$ and $x=\frac{1}{21}$
• C. $x=\frac{7(n-m)}{2m+n}$ and $x=\frac{11}{14}$
• D. $x=\frac{12(n-m)}{2m+3n}$ and $x=\frac{12}{31}$

Answer 1

The correct option is A $x=\frac{5(2n-m)}{2m+3n}$ and $x=\frac{10}{31}$

$\frac{10-3x}{5+2x}=\frac{m}{n}$
Or $n(10-3x)=m(5+2x)$
Or $10n-3xn=5m+2xm$
Or $2xm+3xn=10n-5m$
Or $x(2m+3n)=10n-5m$
Or $x(2m+3n)=5(2n-m)$
Or $x=\frac{5(2n-m)}{2m+3n}$
Given, $3m-4n=2$ Or $3m=2+4n$

Or $3m=2+4\left(2.5\right)=12$

So, $m=4$ ....Since $n=2.5$
So, $x=\frac{5(2\times 2.5-4)}{2\times 4+3\times 2.5}=\frac{5}{15.5}$