Question

The denominator of a fraction is 3 more than the numerator. If 5 is added to both parts the resulting fraction is equivalent to 4/5. find the fraction

Answer 1

Given :

⇝The denominator of a fraction is 3 more than the numerator. If 5 is added to both parts the resulting fraction is equivalent to 4⁄5.

To Find :

⇝ What is the fraction?

ㅤㅤ▬▬▬▬▬▬▬▬▬▬▬▬▬

❍ Let us assume that the numerator and denominator of the fraction is x and x + 3 respectively.

☆ Then, the fraction will be :

ㅤㅤ↦ $\tt{ \dfrac{x}{x + 3} }$

☆ When 5 is added :

ㅤㅤ↦ $\tt{ \dfrac{x + 5}{(x + 3) + 5} }$

★ According to the question,

⇢ $\sf{ \dfrac{x + 5}{(x + 3) + 5} = \dfrac{4}{5} }$

⇢ $\sf{ \dfrac{x + 5}{x + 8} = \dfrac{4}{5} }$

⇢ $\sf{ 5(x + 5) = 4(x + 8) }$

⇢ $\sf{ 5x + 25 = 4x + 32}$

⇢ $\sf{5x - 4x = 32 - 25}$

⇢ $\mathfrak{\underline{\fbox{x = 7}}}$

Therefore, the fraction is :

ㅤㅤ➟ $\bf{ \dfrac{x}{x + 3} }$

ㅤㅤ➟ $\bf{ \dfrac{7}{7 + 3} }$

ㅤㅤ➟ $\fbox{\bf{ \dfrac{7}{10} }}$