Question

Form the pair of linear equations for the following problem and find their solution by substitution method.

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

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

Answer 1

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 =3y`

So, we have two equations

`x - y =26`

`x = 3y`

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

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

` 3y -y =26`

`⇒ 2y = 26`

`⇒ y = 26/2`

`⇒ y = 13`

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

` x -13 =26`

`⇒ x = 13 +26 `

`⇒ x = 39`

Hence, the numbers are 39 and 13.