Question

The numerator of a rational number is less that it’s denominator by 7.If the new number becomes 3/2 when the numerator is tripled and the denominator is increased by 16, find the original number

Pls help me with this question

Answer 1

`(23)/(30)`

Explanation:

let the denominator of the original fraction be x, then

`(x-7)/(x)` ← is the original fraction

After the given changes, that is

`(3(x-7))/(x+16)` =
`(3)/(2)` ( cross- multiply )

6(x - 7) = 3(x + 16) ← distribute parenthesis on both sides

6x - 42 = 3x + 48 ( subtract 3x from both sides )

3x - 42 = 48 ( add 42 to both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Thus

`(30-7)/(30)` =
`(23)/(30)` ← the original rational number