Question

The denominator of a rational number is three less than the numerator. If the denominator is doubled and the denominator is increased by 15, the new number obtained is ⅘. Find the original rational number.​

Answer 1

Answer:

x/x-3

2x/x+12=4/5

Cross multiplying

10x=4x+48

8/56x=48

x=8

8/5

Step-by-step explanation:

I hope this helps u.

Answer 2

Appropriate Question :

The denominator of a rational number is three less than the numerator. If the numerator is doubled and the denominator is increased by 15, the new number obtained is ⅘. Find the original rational number.

$\large\underline{\sf{Solution-}}$

Given that,

• The denominator of a rational number is three less than the numerator.

Let assume that

• Numerator of a fraction be x

So, it means

• Denominator of a fraction is x - 3

So, we have

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Numerator = x} \\ \\ &\sf{Denominator = x - 3}\\ \\ &\sf{Fraction = \dfrac{x}{x - 3} } \end{cases}\end{gathered}\end{gathered}$

According to statement

If the denominator is doubled and the denominator is increased by 15, the new number obtained is ⅘.

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Numerator = 2x} \\ \\ &\sf{Denominator = x - 3 + 15 = x + 12}\\ \\ &\sf{Fraction = \dfrac{2x}{x + 12} } \end{cases}\end{gathered}\end{gathered}$

Thus,

$\rm :\longmapsto\:\dfrac{2x}{x + 12} = \dfrac{4}{5}$

$\rm :\longmapsto\:\dfrac{x}{x + 12} = \dfrac{2}{5}$

$\rm :\longmapsto\:5x = 2x + 24$

$\rm :\longmapsto\:5x - 2x = 24$

$\rm :\longmapsto\:3x = 24$

$\bf\implies \:x = 8$

So,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Numerator = x = 8} \\ \\ &\sf{Denominator = x - 3 = 5}\\ \\ &\sf{Fraction = \dfrac{8}{5} } \end{cases}\end{gathered}\end{gathered}$