Question

A rational number is such that when you multiply it by 5/2 and add 2/3 to its product, you get -7/2.what is the number? ​
Answer please

Answer 1

Answer:

the rational number is -5/3

Step-by-step explanation:

Let the rational number be "a"

According to the question,

⇒ multiply it by 5/2,

      $\frac{5}{2} \times a = \frac{5a}{2}$

⇒ Add 2/3 to the product,

     $\frac{5a}{2} +\frac{2}{3}$

⇒ final result is -7/2,

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

BY SOLVING,

   $\frac{5a}{2} +\frac{2}{3}=\frac{-7}{2} \\\\ \frac{5a}{2} =\frac{-7}{2}-\frac{2}{3}\\\\ \frac{5a}{2} =[\frac{-7}{2} \times \frac{3}{3}]-[\frac{2}{3} \times \frac{2}{2}] \\\\ \frac{5a}{2} =\frac{-21}{6}-\frac{4}{6} \\\\ \frac{5a}{2} =\frac{-21-4}{6} \\\\\frac{5a}{2} =\frac{-25}{6} \\\\ a=\frac{-25}{6} \times \frac{2}{5} \\\\ a=\frac{-5}{3}$

the rational number is -5/3