Question

The sum of two numbers is \[12\] and the difference is \[4\]. How do you find the numbers?

Answer 1

Hint: As the questions says the sum and difference of two numbers is given then let’s assume the two numbers in variable form then just write what we have given and then write down what we have to find in mathematical format or equations. If we have done this then we can easily see the way how to solve further as we will get the two linear equations in two variables then we just have to solve those linear equations and for that we have various methods like elimination, substitution but it is suggested to use elimination as this is quite simple and easy.

Complete step-by-step answer:
Let the first number be \[x\]
Let the other number be \[y\]
According to question
\[x+y=12--(1)\]
\[x-y=4--(2)\]
Now using elimination method
Add \[eq.(1)\] and \[eq.(2)\]
\[\Rightarrow (x+y)+(x-y)=12+4\]
\[\Rightarrow 2x=16\]
\[\Rightarrow x=8\]
Now substituting this value of \[x\] in any of the above equation let put it in \[eq.(1)\]
\[\Rightarrow 8+y=12\]
\[\Rightarrow y=4\]
Thus we have calculated those two numbers.
Hence that are \[4\] and \[8\].

Note: It is important to read the question carefully as in this type of questions if the relation between the numbers is given then the it will leads to the single variable questions otherwise two different variables and just write down in the form of mathematical equations what the question has given and it will automatically leads to a proper solution.