Question

Find the value of $n$:
$3(n-5)+5n=7(a-n)-2(n-b)$, where $a$ and $b$ are constants.

• A. $n=\frac{15+7a+2b}{17}$
• B. $n=\frac{17-2a+7b}{15}$
• C. $n=\frac{17-7a+2b}{11}$
• D. $n=\frac{15-7a-2b}{13}$

Answer 1

The correct option is A $n=\frac{15+7a+2b}{17}$

The given equation is,
$3(n-5)+5n=7(a-n)-2(n-b)\Rightarrow 3n-15+5n=7a-7n-2n+2b\Rightarrow 8n-15=-9n+7a+2b\Rightarrow 8n+9n=15+7a+2b\Rightarrow 17n=15+7a+2b\Rightarrow n=\frac{15+7a+2b}{17}$