Question

The denominator of a fraction is 1 less than twice its numerator. If 1 is added to numerator and denominator respectively, the ratio of numerator to denominator is 3:5. Find the fraction​

Answer 1

Step-by-step explanation:

Here let numerator= x

and dominator= 2x-1

x+1 = 3:5

2x-1+1

x+1 = 3

2x 5

5(x+1)= 6x

5x+5=6x

5= 6x-5x

x= 5

denominator= 2x-1= 2×5-1= 10-1= 9

therefore the faction is 5/9

Answer 2

Basic Concept :-

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.

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

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{numertor = x} \\ &\sf{denominator = 2x - 1} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: Fraction- \begin{cases} &\sf{\dfrac{x}{2x - 1} }\end{cases}\end{gathered}\end{gathered}$

↝ According to statement,

↝ If 1 is added to each numerator and denominator,

$\begin{gathered}\begin{gathered}\bf\: Then-\begin{cases} &\sf{numertor = x + 1} \\ &\sf{denominator = 2x - 1 + 1 = 2x} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: Fraction- \begin{cases} &\sf{\dfrac{x + 1}{2x} }\end{cases}\end{gathered}\end{gathered}$

↝ It is given that, the ratio of numerator to denominator is 3 : 5.

$\rm :\longmapsto\:\dfrac{x + 1}{2x} = \dfrac{3}{5}$

$\rm :\longmapsto\:5x + 5 = 6x$

$\rm :\longmapsto\:6x - 5x = 5$

$\bf\implies \:x = 5$

$\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{numertor = 5} \\ &\sf{denominator = 2 \times 5 - 1 = 9} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: So, \: Fraction- \begin{cases} &\sf{\dfrac{5}{9} }\end{cases}\end{gathered}\end{gathered}$