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

Last updated date: 20th Jul 2024
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Hint: Using the equation of difference between two numbers and one number is thrice the other number, determine the two numbers. Then, find the sum of these two numbers.

Complete step-by-step answer:
Let us assume the two numbers to be x and y with x greater than y.
It is given that the difference between the two numbers is 26. Hence, we have:
\[x - y = 26.........(1)\]
It is also given that one of the numbers is three times the other number. Since, x is the greatest number of the two, x is 3 times y. Hence, we have:
\[x = 3y............(2)\]
We have two equations with two unknowns x and y. Hence, we can solve them
Substitute equation (2) in equation (1) to get:
\[3y - y = 26\]
We know that 3y – y is 2y, hence, we have:
\[2y = 26\]
Taking 2 to the other side and dividing with 26, we get 13.
\[y = \dfrac{{26}}{2}\]
\[y = 13...........(3)\]
Using equation (3) in equation (2), we get the value of x.
\[x = 3(13)\]
We know the value of 3(13) is 39, hence, we have:
\[x = 39..........(4)\]
We now need to find the sum of these two numbers x and y.
From equation (3) and equation (4), we can add x and y to get the desired answer.
\[x + y = 39 + 13\]
\[x + y = 52\]
Hence, the value of the sum of the two numbers is 52.

Note: We can cross check your answer by substituting the value of the variables in the equations and see if they satisfy the expressions. This will help in understanding whether we got the correct answer or not.