Question

The numerator of a fraction is 3 less than than its denominator. If 3 is added to the numerator and 4 is added to the denominator, the fraction becomes 5/9 Find the fraction.​

Answer 1

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

Given that,

• The numerator of a fraction is 3 less than than its denominator.

Let assume that

• Denominator of a fraction be x

So,

• Numerator of a fraction is x - 3

Thus,

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

According to second condition

If 3 is added to the numerator and 4 is added to the denominator, the fraction becomes 5/9

So, we have now

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Denominator = x + 4} \\ \\ &\sf{Numerator = x - 3 + 3 = x} \\ \\ &\sf{Fraction = \dfrac{x}{x + 4} } \end{cases}\end{gathered}\end{gathered}$

Now,

$\rm :\longmapsto\:\dfrac{x}{x + 4} = \dfrac{5}{9}$

$\rm :\longmapsto\:9x = 5x + 20$

$\rm :\longmapsto\:4x = 20$

$\rm \implies\:x = 5$

Hence,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Denominator = 5} \\ \\ &\sf{Numerator = 5 - 3 = 2} \\ \\ &\sf{Fraction = \dfrac{2}{5} } \end{cases}\end{gathered}\end{gathered}$

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Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.