Question

The numerator of a rational number is less than
Its denominator by 4.if the numerator and
denominator both are increased by 2. The number
becomes 5/9. Find the number..
it's urgent please answer​

Answer 1

Given :-

• The numerator of a rational number is less than its denominator by 4.

• If the numerator and denominator both are increased by 2. The number becomes 5/9

To Find :-

• The number

Concept Used

Formulation of system of Linear Equations 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 mentioned what the variable represents.

3. Carry out the plan and solve the problem.

Solution :-

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{denominator = x} \\ &\sf{numerator = x - 4} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:Hence \: number \: is-\begin{cases} &\sf{\dfrac{x - 4}{x} }\end{cases}\end{gathered}\end{gathered}$

Now,

According to statement,

If the numerator and denominator both are increased by 2.

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{denominator = x + 2} \\ &\sf{numerator = x - 2} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:Hence \: number \: is-\begin{cases} &\sf{\dfrac{x - 2}{x + 2} }\end{cases}\end{gathered}\end{gathered}$

According to statement, number becomes 5/9

$\bf\implies \:\dfrac{x - 2}{x + 2} = \dfrac{5}{9}$

$\rm :\longmapsto\:9(x - 2) = 5(x + 2)$

$\rm :\longmapsto\:9x - 18 = 5x + 10$

$\rm :\longmapsto\:9x - 5x = 18 + 10$

$\rm :\longmapsto\:4x = 28$

$\bf\implies \:x = 7$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{denominator = x = 7} \\ &\sf{numerator = x - 4 = 7 - 4 = 3} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:Hence \: number \: is-\begin{cases} &\sf{\dfrac{3}{7} }\end{cases}\end{gathered}\end{gathered}$

Answer 2

Answer:

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