Question

The numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator ,the fraction becomes 3/4.find the fraction​

Answer 1

Answer:

Denominator =x=5

Numerator =x-2=3

Step-by-step explanation:

• Let denominator be x
• numerator = (x-2)
• If 3 is added to numerator and denominator, then.

x-2-3/x+3=3/4

x+1/x+3=3/4

4(x+1)=3(x+3)

4x+4=3x+9

x=5

• Denominator =x=5
• Numerator =x-2=3

Answer 2

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

Basic Concept Used :-

Writing System of Linear Equation from Word Problems

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.

Let's solve the problem now!!

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

$\begin{gathered}\begin{gathered}\bf \: So- \begin{cases} &\sf{fraction \: = \: \dfrac{x - 2}{x} }\end{cases}\end{gathered}\end{gathered}$

According to statement,

• When 3 is added to both numerator and denominator,

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{denominator = x + 3} \\ &\sf{numerator = x - 2 + 3 = x + 1} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: So- \begin{cases} &\sf{fraction \: = \: \dfrac{x + 1}{x + 3} }\end{cases}\end{gathered}\end{gathered}$

According to statement,

$\rm :\longmapsto\:\dfrac{x + 1}{x + 3} = \dfrac{3}{4}$

$\rm :\longmapsto\:4x + 4 = 3x + 9$

$\bf\implies \:x \: = \: 5$

$\begin{gathered}\begin{gathered}\bf \: So- \begin{cases} &\sf{fraction \: = \: \dfrac{x - 2}{x} = \dfrac{5 - 2}{5} = \dfrac{3}{5}}\end{cases}\end{gathered}\end{gathered}$