Question

when a rational number is multiplied by
$\frac{3}{4} \: and \: added \: to \: \frac{2}{7} gives \: \frac{5}{7} \: .find \: the \: number$

Answer 1

Solutions :-



Let the certain rational number be x


A/q

$= > x \times \frac{3}{4} + \frac{2}{7} = \frac{5}{7} \\ \\ = > \frac{3x}{4} + \frac{2}{7} = \frac{5}{7} \\ \\ = > \frac{21x + 8}{28} = \frac{5}{7 } \\ \\ = > 7(21x + 8) = 28(5) \\ \\ = > 147x + 56 = 140 \\ \\ = > 147x = 140 - 56 \\ \\ = > 147x = 84 \\ \\ = > x = \frac{84}{147} = \frac{4}{7}$


Now,
Verification :-

Putting the value of x =>


$= > \frac{4}{7} \times \frac{3}{4} + \frac{2}{7} = \frac{5}{7} \\ \\ = > \frac{12}{28} + \frac{2}{7} = \frac{5}{7} \\ \\ = > \frac{12+ 8}{28} = \frac{5}{7 } \\ \\ = > \frac{20}{28} = \frac{5}{7} \\ \\ = > \frac{5}{7} = \frac{5}{7}$

L.H.S = R.H.S

Verified ✔✔




Hence,
$\bold {The \: number\: is\: \frac{4}{7} }$