Question

One number exceeds the other by 12. If their sum is 72 find the numbers?

Answer 1

Hint: In order to solve the unknown numbers, let them be $ x $ and $ y $ . Form a mathematical expression from the expression given in the question as $ x - y = 12 $ and $ x + y = 72 $ .To solve these two equations , add them to get the value of x and later put this value of x in either of the equations to obtain the value of y.

Complete step-by-step answer:
We are given a statement “One number exceeds the other by 12”.
Lets first convert this statement into mathematical expression.
Let both the unknown numbers be $ x $ and $ y $
In order to write any mathematical expression from some statement, we must first find the relationship and the quantities specified.
Here in this question the relation x and y is that the x exceeds or we can say is greater than y by 12.
So, this means x is equal to sum of y and 12
Hence,
 $ x = y + 12 $
 $ x - y = 12 $ ----(1)
According to the question, the sum of both the unknown number i.e. x and y is given as 72
 $ x + y = 72 $ ----(2)
Now adding equation (1) with equation (2),we get
\[x + x + y - y = 72 + 12\]
Combining like terms on both of the sides, we get
\[2x = 84\]
Dividing both sides of the equation with the coefficient of x i.e. 2
\[
  \dfrac{{2x}}{2} = \dfrac{{84}}{2} \\
\Rightarrow x = 42 \;
 \]
Now putting this value of $ x = 42 $ in equation (1)
 $
\Rightarrow x - y = 12 \\
\Rightarrow 42 - y = 12 \\
\Rightarrow y = 42 - 12 \\
\Rightarrow y = 30 \;
  $
Therefore, the unknown numbers $ x $ and $ y $ are equal to 42 and 30 respectively
So, the correct answer is “x=42 AND y=30”.

Note: 1.Mathematical equation: A Mathematical equation can be defined as the mathematical statement which contains an equal symbol $ = $ in between two algebraic expressions that share the same value .
A algebraic expression can contain any number of variables generally we take 2-3 variables
Let assume a expression
 $ 5x + 9 = 24 $
It is a mathematical equation having LHS (Left-Hand-Side) equal to RHS (Right-Hand-Side)
Where $ x $ is the variable
5 is the coefficient of variable $ x $
And $ 24,9 $ are the constants
2. Read the statement carefully in order to convert them into mathematical expressions.
3.Solution of two linear equations can be done by using elimination method , substitution method and cross multiplication method .