Question

The sum of the two numbers is 26. One of the numbers is 2 more than twice the other. Find the numbers.

Answer 1

Hint: Let us assume the first number to be $x$ , the other number becomes $26-x$.
we can develop an equation using the data given in the question . Use both these equations to find the value of $x$.

Complete step-by-step answer:
Before proceeding we must be familiar with the terms, like the left-hand-side and the right-hand-side, how to solve linear equations, what are the rules to solve the equations when there are terms both on the left-hand-side and right-hand-side, what happens to the terms when we take it from right-hand-side to the left-hand-side.
In this question we have been given, the sum of the two numbers is 26. One of the numbers is 2 more than twice the other then we have to find out the numbers.
Let us assume the first number is $x$ .
Then the other number becomes $26-x$.
In question, it is given that one of the numbers is 2 more than twice the other.

The equation becomes, $x=2+2\left( 26-x \right)$.
Opening the brackets, we get,
$\therefore x=2+2\times 26-2x$

Now taking the variables on the left-hand side we get,
$\Rightarrow x+2x=2+52$
$\Rightarrow 3x=54$
$\Rightarrow x=\dfrac{54}{3}$

After cancelling we get,
$\therefore x=18$

Therefore, the first number is $18$.
The other number is given by $26-x=26-18$
Therefore, the other number is $8$. Hence, the required numbers are $18$ and $8$.

Note: We must be very careful about the sign when we are taking the terms from left-hand-side to right-hand-side and vice-versa. We can cross-check the answer by putting the value of the answer and verifying it with the question.