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

`(29)/(58)`

Explanation:

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

original fraction =
`(x)/(2x)`

subtracting 3 from numerator and adding 7 to denominator , gives

`(x-3)/(2x+7)` =
`(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 =
`(29)/(58)`