The difference between two numbers is 26 and one number is three times the other.

Solution:

Let the numbers are $x$ and $y$. One of them must be greater than or equal to the other. Let us assume that $x$ is greater than or equal to $y$.

The difference between the two numbers is 26 . Thus, we have $x-y=26$

One of the two numbers is three times the other number. Here, we are assuming that $x$ is greater than or equal to $y$. Thus, we have $x=3 y$

So, we have two equations

$x-y=26$

$x=3 y$

Here $x$ and $y$ are unknowns. We have to solve the above equations for $x$ and $y$.

Substituting $x=3 y$ from the second equation in the first equation, we get

$3 y-y=26$

$\Rightarrow 2 y=26$

$\Rightarrow y=\frac{26}{2}$

$\Rightarrow y=13$

Substituting the value of y in the first equation, we have

$x-13=26$

$\Rightarrow x=13+26$

 

$\Rightarrow x=39$

Hence, the numbers are 39 and 13.