Question

The sum of $3$ numbers is $61$. The second number is $5$ times the first. While the $3rd$ is $2$ less than the first. How do you find the numbers?

Answer 1

Hint: In this question, there are three equations and we have to find three variables. We can easily do this by substitution method in which we find one variable in terms of another. Also in this question, we can find the second and third variable in terms of first and then we put all these values in the first equation to get to the answer.

Complete step-by-step answer:
In the above question, we have to find the three numbers.
So, let’s take the three numbers x, y, and z.
Now, it is given that the sum of $3$ numbers is $61$.
Therefore,
$x + y + z = 61...............\left( 1 \right)$
It is also given that the second number is $5$ times the first.
Therefore,
$ \Rightarrow y = 5x.......\left( 2 \right)$
Also, the $3rd$ is $2$ less than the first.
Therefore,
$ \Rightarrow z = x - 2..................\left( 3 \right)$
Now, put the value of y and z from equation second and third in the first equation.
Therefore, on putting the values we get
$ \Rightarrow x + 5x + x - 2 = 61$
Now, transpose two to the right-hand side and add all the variable terms.
$ \Rightarrow 7x = 61 + 2$
$ \Rightarrow 7x = 63$
Now divide both sides by $7$.
$ \Rightarrow x = 9$
Now, we can find the value of the other two variables also by putting this value in the second and third equation.
Therefore,
$ \Rightarrow y = 5x = 5 \times 9 = 45$
Also,
$ \Rightarrow z = x - 2 = 9 - 2 = 7$
Therefore, the value of three variables is $9\,,\,45\,and\,7.$

Note: This question is an example of a linear equation in three variables. We can also do this question by elimination method in which we make the coefficient of a variable in two equations same by multiplying with appropriate value and then subtracting these two equations.