Question

. Find two consecutive odd numbers such that the smaller number exceeds one-third of the larger
by 20.​

Answer 1

Basic Concept Used :-

Writing Systems 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.

Let's solve the problem now!!!

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

$\begin{gathered}\begin{gathered}\sf\: Let \: consecutive \: odd \: numbers \: be-\begin{cases} &\sf{x} \\ &\sf{x + 2} \end{cases}\end{gathered}\end{gathered}$

☆ According to statement, smaller number exceeds one third of larger number by 20.

$\purple{\bf :\longmapsto\:x - \dfrac{1}{3}(x + 2) = 20}$

$\rm :\longmapsto\:x - \dfrac{x + 2}{3} = 20$

$\rm :\longmapsto\:\dfrac{3x - (x + 2)}{3} = 20$

$\rm :\longmapsto\:\dfrac{3x - x - 2}{3} = 20$

$\rm :\longmapsto\:\dfrac{2x - 2}{3} = 20$

$\rm :\longmapsto\:2x - 2 = 60$

$\rm :\longmapsto\:2x = 62$

$\bf\implies \:x = 31$

Hence,

$\begin{gathered}\begin{gathered}\sf\: Consecutive \: odd \: numbers \: be-\begin{cases} &\sf{x = 31} \\ &\sf{x + 2 = 33} \end{cases}\end{gathered}\end{gathered}$