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# The number is that of which the third part exceeds the fifth part by $4?$

Last updated date: 15th Jul 2024
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Hint: Linear Equation: Linear equation is the equation of first order. These equations are defined for the line in the coordinate system. Linear equations are represented by $ax + b = 0$ where ‘a’ are integers, x are variables and c are constant for the equation. This equation shows the line is linear and straight.
First we try to write the equation as per given statement and then we simply give an equation and we will get a simplified linear equation.

Complete step by step solution:
Given,
The given equation is a linear equation of a single variable.
According to the question.
$\Rightarrow \dfrac{n}{3} = \dfrac{n}{5} + 4$
Simplify the equation
$\Rightarrow \dfrac{n}{3} = \dfrac{{n + 20}}{5}$
Again
$\Rightarrow 5n = 3 \times \left( {n + 20} \right)$
$\Rightarrow 5n = 3n + 60$
$\Rightarrow 5n - 3n = 60$
$\Rightarrow 2n = 60$
$\Rightarrow n = \dfrac{{60}}{2}$
$\Rightarrow n = 30$
Hence the value of $n = 30.$
So, the correct answer is “ $n = 30$”.

Note: There are various types of linear equations. One variable and two variable linear equations. For two variable linear equations, $ax + by + c = 0$ where a and b are integers, x and y are variables and c are constant. It is used for solving age problems, speed and time, and geometry problems. And solving the word problems.