Question

Divide $4500$ into two parts such that $5\% $ the first part is equal to $10\% $ the second part?

Answer 1

Hint: So for solving it first we will assume two variables and then by using the statement given in this question which will be $5\% {\text{ of x = 10% of y}}$. And then on solving both the values of variables, we will get the required answer.

Complete step-by-step answer:
Let us assume that $x$ & $y$ is divided into parts $4500$.
So it can also be written as
$x + y = 4500$ , and we will name its equation $1$.
Also from the question, it is given that
$ \Rightarrow 5\% {\text{ of x = 10\% of y}}$
So on solving, infraction it can be written as
$ \Rightarrow \dfrac{{5x}}{{100}} = \dfrac{{10y}}{{100}}$
And on solving the above equation, we get
$ \Rightarrow x = 2y$
Presently putting the above estimation of $x$ in condition$1$, we get
$ \Rightarrow 2y + y = 4500$
Now on adding the LHS, we get
$ \Rightarrow 3y = 4500$
So solving for the value of$y$, we get
$ \Rightarrow y = \dfrac{{4500}}{3}$
And it will be equal to
$ \Rightarrow y = 1500$
Presently putting the above estimation of $y$ in condition$1$, we get
$ \Rightarrow x + 1500 = 4500$
Now, solving for the value of $x$and for this taking the $1500$ to the RHS and solve for it, we get
$ \Rightarrow x = 4500 - 1500$
And therefore the $x$ will be equal to
$ \Rightarrow x = 3000$
Therefore, $4500$ is being divided into two parts $3000{\text{ and 1500}}$.

Additional information:
Sometimes by using the other method also we solve such problems for example by using the elimination method or by using the substitution method also we will be able to solve the problem of the linear equation. More methods exist like cross multiplication, which is one of them.

Note: This type of problem is solvable by comparing the equation which will always be made by the statement given in the question. And then equating them we will get the solution. So the fundamental piece of this inquiry is to outline a condition that will legitimize the assertion.