Question

If solution of the equation $\frac{2x}{5}-\frac{1}{2}=5$ is $x=\frac{a}{b},$ where fraction $\frac{a}{b}$ is in its simplest form, then

• A. $a=31$
• B. $b=4$
• C. $a=55$
• D. $b=3$

Answer 1

Answer: (B), (C)

$a=55$

Given, the equation is $\frac{2x}{5}-\frac{1}{2}=5.$

Step 1: Add both sides of the equation by $\frac{1}{2}$ in order to remove the $\frac{1}{2}$ on the left hand side.
$\Rightarrow \frac{2x}{5}-\frac{1}{2}+\frac{1}{2}=5+\frac{1}{2}(\because \frac{1}{2}-\frac{1}{2}=0)$
$\Rightarrow \frac{2x}{5}=5+\frac{1}{2}$
$\Rightarrow \frac{2x}{5}=\frac{5\times 2}{1\times 2}+\frac{1}{2}\left(\text{making the denominators equal for}5\text{and}\frac{1}{2}\right)$
$\Rightarrow \frac{2x}{5}=\frac{10}{2}+\frac{1}{2}$
$\Rightarrow \frac{2x}{5}=\frac{10+1}{2}$
$\Rightarrow \frac{2x}{5}=\frac{11}{2}$

Step 2: Multiply both the sides by 5
$\Rightarrow \frac{2x}{5}\times 5=\frac{11}{2}\times 5$
$\Rightarrow 2x=\frac{55}{2}$

Step 3: Divide both the sides by 2
$\Rightarrow \frac{2x}{2}=\frac{\frac{55}{2}}{2}$
$\Rightarrow x=\frac{55}{2\times 2}$
$\Rightarrow x=\frac{55}{4}=\frac{a}{b}$
$\therefore a=55,b=4$