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# Find two numbers such that one of them exceeds the other by $9$ and their sum is $81$.

Last updated date: 25th Jul 2024
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Hint: We are given here, two numbers such that one number exceeds the other by $9$ and their sum is $81$. We have to find those numbers. We do this by making this an equation of one variable. We consider one of the numbers as a variable and we get the other number in terms of that variable as well. Then we try to find the value of that variable. Once we get that value, we can easily find both the numbers.

Complete step-by-step solution:
Here, we have to find the value of two numbers who differ by $9$ and their sum is $81$. We consider the smaller number to be a variable say $x$. Then according to the question the greater number would be $x + 9$. Now since we know that the sum of both the numbers are $81$, we say that,
$(x + 9) + x = 81$
On moving forward, we get
$2x + 9 = 81 \\ \Rightarrow 2x = 81 - 9 \\ \Rightarrow 2x = 72 \\ \Rightarrow x = \dfrac{{72}}{2} \\ \Rightarrow x = 36$
Hence the value of the smaller number is $36$. Now using this we will get the value of greater number by putting $x = 36$ in $x + 9$ as,
$36 + 9 = 45$
Hence, we get the value of both the required numbers as $36$ and $45$.

Note: Whenever two values are to be found and the relations between both the values are given, we solve the question using the equation of one variable. If the relations between the values to be found are not given then, only we will use the equation in two variables.