Question : -
The sum of two consecutive odd numbers is 24. Find the numbers .
Given : -
- Sum of two consecutive odd no. = 24
To Find : -
We have to find the numbers .
Concept : -
In this question we have to find the numbers by assuming the numbers and forming equations to finally get the appropriate answer .
To Assume : -
- Let second odd no. be x + 2
So let's get started by solving : -
[tex] \longrightarrow \: x + 2 + x= 24[/tex]
Now adding them ,
[tex] \longrightarrow \: 2x + 2 = 24[/tex]
Now taking 2 common ,
[tex] \longrightarrow \: 2(x + 1) = 24[/tex]
Now dividing 24 by 2 ,
[tex] \longrightarrow \: x + 1 = \frac{24}{2} [/tex]
We get ,
[tex] \longrightarrow \: x + 1 = 12[/tex]
Now transposing 1 to right hand side ,
[tex] \longrightarrow \: x = 12 - 1[/tex]
So ,
[tex] \longrightarrow \: \boxed{\bold{ x = 11}}[/tex]
Therefore value of first number is 11 .
Now , other consecutive no. be x + 2 . So
Therefore value of second number is 13 .
Verifying :
According to question sum of two consecutive no. is 24. So :
Therefore our answer is valid .
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