Question

The difference between two numbers is 26 and one number is three times the other. Find the sum of these numbers.

Answer 1

Hint: Assume that the two numbers are \[x\] and \[y\]. The difference between the two numbers is 26 so, \[x-y=26\]. Also, one number is thrice of other so, \[x\] must be three times of \[y\]. Now, we have two equations and two variables which can be solved easily. Calculate the value of \[x\] and \[y\] .

Complete step by step answer:
According to the question, we are given that there are two numbers and the difference between the two numbers is 26. Also, one number is three times the other.
First of all, let us assume that the first number is \[x\] while the second number is \[y\] .
Since the difference between the two numbers is 26 and the two numbers are \[x\] and \[y\] so, the difference between the numbers \[x\] and \[y\] must also be equal to 26.
\[x-y=26\] ……………………………………….(1)
Also, we are given that the first number is three times the other so, \[x\] must be equal to three times \[y\] .
\[x=3y\] …………………………………………..(2)
Now, on substituting \[x\] by \[3y\] in equation (1), we get
\[\begin{align}
  & \Rightarrow 3y-y=26 \\
 & \Rightarrow 2y=26 \\
 & \Rightarrow y=\dfrac{26}{2} \\
\end{align}\]
\[\Rightarrow y=13\] ……………………………..(3)
Now, on putting the value of \[y\] in equation (2), we get
\[\Rightarrow x=3\times 13\]
\[\Rightarrow x=39\] ………………………………………..(4)
From equation (3) and equation (4), we have
The value of first number = 39.
The value of the second number = 13.
Therefore, the two numbers are 13 and 39.

Note:
Whenever this type of question appears, then always approach by assuming two numbers in terms of the variable \[x\] and \[y\] . By assuming this, we get a linear equation in two variables which can be solved easily.