Question

What is the sum of two numbers is $28$ and their difference is $4$?

Answer 1

Hint: To solve this type of question, first we will assume any two numbers x and y and then we will apply the condition as given in the question. When we will apply the condition then we get two linear equation with two variable, and we know very well, if any equation which can be put in the form $ax+by+c=0$, where a, b, and c are real numbers, and a and b are not zero, is called a linear equation in two variables.

Complete step by step solution:
Let's suppose the two numbers x and y
Now according to the question the first condition is that the sum of two numbers is $28$, if we write this condition in mathematical way, then we get
$\Rightarrow x+y=28...........(1)$
Now the second condition is that the difference of two numbers is $4$, if we also write this condition in mathematical way, then we get
$\Rightarrow x-y=4............(2)$
Now we will add these two equations so that we can get the value of two numbers which are x and y.
Now adding equation (1) and (2), then we get
$\Rightarrow x+y+x-y=28+4$
Here we can see both y are in opposite sign, so they both cancel out, then we get
$\begin{align}
  & \Rightarrow 2x=32 \\
 & \Rightarrow x=16 \\
\end{align}$
The first number is $16$ , now in order to find the second number we will put this value of x in equation (1), we get
$\begin{align}
  & \Rightarrow 16+y=28 \\
 & \Rightarrow y=28-16 \\
 & \Rightarrow y=12 \\
\end{align}$
Hence we get both numbers which satisfy both conditions.

Note: we can also check if our numbers which we get above are correct or not. For this but the both numbers in any of the given condition, let put the values in the first condition which is as:
$\Rightarrow x+y=28$ , put $x=16,y=12$ , then we get
$\begin{align}
  & \Rightarrow 16+12=28 \\
 & \Rightarrow 28=28 \\
\end{align}$
Hence our values are correct.