Question

A rational number is such that when you multiply it by $\frac{5}{2}$ and add $\frac{2}{3}$ to the product, you get $-\frac{7}{12}$. What is the number?

• A. $-\frac{2}{3}$
• B. $-\frac{1}{2}$
• C. $-\frac{1}{3}$
• D. $-\frac{2}{5}$

Answer 1

The correct option is B $-\frac{1}{2}$

Let the rational number be $x$.

Now this rational number is multiplied by $\frac{5}{2}$ and the resultant is added to $\frac{2}{3}$.

According to the question, we have

$\frac{5}{2}x+\frac{2}{3}=\frac{-7}{12}$

$\frac{5}{2}x=-\frac{2}{3}-\frac{7}{12}$

$\frac{5}{2}x=\frac{-8-7}{12}$

$x=-\frac{15}{12}\times \frac{2}{5}$

$\therefore x=-\frac{1}{2}$