Question

What two numbers sum 20 but have a difference of 12?

Answer 1

Hint: In this problem, we have to find the two numbers, which when added up gives 20 and the difference between them will be 12. We can first assume the two numbers as x and y, we can then form two equations and using the elimination formula, we can eliminate one of the variables and find the value of the other variable. We can then substitute the value of the resulting variable in one of the equations to find the value of the second variable.

Complete step by step answer:
Here we have to find the two numbers which when added up gives 20 and the difference between them will be 12.
We can now assume the two numbers as x and y.
We are given that, the two numbers added to give 20 and subtracted to give 12, we can write it as,
\[\begin{align}
  & \Rightarrow x+y=20......\left( 1 \right) \\
 & \Rightarrow x-y=12......\left( 2 \right) \\
\end{align}\]
We can now elimination method and add (1) and 2, we get
\[\begin{align}
  & \Rightarrow x+y-20+x-y-12=0 \\
 & \Rightarrow 2x-32=0 \\
 & \Rightarrow x=16 \\
\end{align}\]
The value of x is 16.
We can now substitute this value in (1), we get
\[\begin{align}
  & \Rightarrow 16+y=20 \\
 & \Rightarrow y=4 \\
\end{align}\]
Therefore, the required two numbers are 16 and 4.

Note: We should know to write the given sentence in a mathematical equation, to simplify them in order to find the required values. We can now check for the answers to be correct, by substituting the value of x and y in the equations (1) and (2), we get
\[\begin{align}
  & \Rightarrow 16+4=20 \\
 & \Rightarrow 16-4=12 \\
\end{align}\]
Therefore, the answers are correct.