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?

Given :

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

To do :

We have to find the number.

Solution :

Let the number be x.

A number is multiplied by \( \frac{5}{2} \) and \( \frac{2}{3} \) is added to the product.

So, $x \times \frac{5}{2} = \frac{5x}{2}$

The result is added to $\frac{2}{3}$, we will get,

$\frac{5x}{2}+\frac{2}{3}=\frac{5x(3)+2(2)}{6}=\frac{15x+4}{6}$.

Therefore,

$\frac{15x+4}{6}= -\frac{7}{12}$

$12(15x+4) = -7(6)$

$2(15x+4) = -7$

$30x+8= -7$

$30x=-7-8$

$x=\frac{-15}{30} $

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

Therefore, the required number is $-\frac{1}{2}$.

Tutorialspoint

e

Updated on: 10-Oct-2022

30 Views

Kickstart Your Career

Get certified by completing the course

Get Started