Question

The denominator of a rational numbers is twice it’s numerator if the numerator is decreased by 3 and the denominator increased by 7 the number obtained is 2/5 find the rational number

Answer 1

Answer:

$\frac{29}{58}$

Step-by-step explanation:

let x be the numerator of the rational number then 2x is the denominator

original fraction = $\frac{x}{2x}$

subtracting 3 from numerator and adding 7 to denominator , gives

$\frac{x-3}{2x+7}$ = $\frac{2}{5}$ ( cross- multiply )

5(x - 3) = 2(2x + 7) ← distribute parenthesis on both sides )

5x - 15 = 4x + 14 ( subtract 4x from both sides )

x - 15 = 14 ( add 15 to both sides )

x = 29

rational number = $\frac{29}{58}$