Answer
Verified
328.3k+ views
Hint- Here, we will be assuming the first three parts of 243 as three different variables and then will be using a substitution method to solve the obtained three equations in three variables.
Here, we have to divide 243 into three parts. Let us assume that the first part be $x$, the second part be $y$ and the third part be $z$.
Clearly, $x + y + z = 243{\text{ }} \to {\text{(1)}}$
Given, half of the first part, one-third part of the second part and one-fourth of the third part are all equal to each other i.e., $\dfrac{x}{2} = \dfrac{1}{3}\left( y \right) = \dfrac{1}{4}\left( z \right) \Rightarrow \dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4}$
Here, we will represent all the other variables in terms of variable x.
Now, considering $\dfrac{x}{2} = \dfrac{y}{3}$, we can write variable y in terms of variable x as under
$ \Rightarrow y = \dfrac{{3x}}{2}{\text{ }} \to (2{\text{)}}$
Now, considering $\dfrac{x}{2} = \dfrac{z}{4}$, we can write variable z in terms of variable x as under
$ \Rightarrow z = \dfrac{{4x}}{2} \Rightarrow z = 2x{\text{ }} \to {\text{(3)}}$
Substitute equations (2) and (3) in equation (1), we gwt
$x + \dfrac{{3x}}{2} + 2x = 243 \Rightarrow \dfrac{{2x + 3x + 4x}}{2} = 243 \Rightarrow 9x = 486 \Rightarrow x = 54$
Put the above obtained value of x in equation (2), we get
$ \Rightarrow y = \dfrac{{3 \times 54}}{2} = 81$
Put the above obtained value of x in equation (3), we get
$ \Rightarrow z = 2 \times 54 = 108$
Hence, 243 is divided into 54, 81 and 108 as the three parts respectively.
Therefore, 243 is divided into three parts such that the half of the first part which is 54, one-third of the second part which is 81 and one-fourth of the third part which is 108 are all equal.
Note- In these type of problems, according to the problem statement we will obtain three equations in three variables and then from two of the above equations, we will be representing the two different variables (y and z) in terms of the other variable (x) and then substituting these values in the third equation to solve for the value of x.
Here, we have to divide 243 into three parts. Let us assume that the first part be $x$, the second part be $y$ and the third part be $z$.
Clearly, $x + y + z = 243{\text{ }} \to {\text{(1)}}$
Given, half of the first part, one-third part of the second part and one-fourth of the third part are all equal to each other i.e., $\dfrac{x}{2} = \dfrac{1}{3}\left( y \right) = \dfrac{1}{4}\left( z \right) \Rightarrow \dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4}$
Here, we will represent all the other variables in terms of variable x.
Now, considering $\dfrac{x}{2} = \dfrac{y}{3}$, we can write variable y in terms of variable x as under
$ \Rightarrow y = \dfrac{{3x}}{2}{\text{ }} \to (2{\text{)}}$
Now, considering $\dfrac{x}{2} = \dfrac{z}{4}$, we can write variable z in terms of variable x as under
$ \Rightarrow z = \dfrac{{4x}}{2} \Rightarrow z = 2x{\text{ }} \to {\text{(3)}}$
Substitute equations (2) and (3) in equation (1), we gwt
$x + \dfrac{{3x}}{2} + 2x = 243 \Rightarrow \dfrac{{2x + 3x + 4x}}{2} = 243 \Rightarrow 9x = 486 \Rightarrow x = 54$
Put the above obtained value of x in equation (2), we get
$ \Rightarrow y = \dfrac{{3 \times 54}}{2} = 81$
Put the above obtained value of x in equation (3), we get
$ \Rightarrow z = 2 \times 54 = 108$
Hence, 243 is divided into 54, 81 and 108 as the three parts respectively.
Therefore, 243 is divided into three parts such that the half of the first part which is 54, one-third of the second part which is 81 and one-fourth of the third part which is 108 are all equal.
Note- In these type of problems, according to the problem statement we will obtain three equations in three variables and then from two of the above equations, we will be representing the two different variables (y and z) in terms of the other variable (x) and then substituting these values in the third equation to solve for the value of x.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The cell wall of prokaryotes are made up of a Cellulose class 9 biology CBSE
What organs are located on the left side of your body class 11 biology CBSE
Select the word that is correctly spelled a Twelveth class 10 english CBSE
a Tabulate the differences in the characteristics of class 12 chemistry CBSE