Question

The sum of two numbers is 99. If one exceeds the other by 9, find the numbers.

Answer 1

Hint:
Here we assume the first number as a variable and use the concept of linear equation to write the second number in form of a variable. Then we write an equation where we add both the numbers and equate it with 99. And we will solve the equation to find the value of two numbers.

Complete step by step solution:
Here we will assume the first number is $x$.
Then we know one number is 9 more than the other number.
So, the second number will be the first number plus the 9 of the first number.
So, the second number will be $x+9$.
We are given the question statement that the sum of two numbers is 99.
So, to get a linear equation we will add the two numbers and equate it to 99.
$\Rightarrow x+x+9=99$
We will combine all the terms with x.
$\Rightarrow 2x+9=99$
Now we will subtract 9 from both sides of the equation
$\Rightarrow 2x=99-9 \\
\Rightarrow 2x=90$
We will divide L.H.S. and R.H.S. of the equation by 2.
$\Rightarrow x=\dfrac{90}{2}=45$
 Therefore, the first number is 45.
Now we know the second number can be determined by $x+9$.
Substituting the value of x as 45 in the equation $x+9$ we get:
So, the second number is 54.

Therefore, the numbers whose sum of is 99 and one exceeds the other by 9 are 45 and 54.

Note:
In most of the algebraic problems, it is important to convert the problem in English into mathematical equations. Once that is done, the question becomes easy to solve. Generally, an equation with one variable or two equations with the variables can be solved by a simple substitution or elimination method.