Question

the sum of three consecutive odd number is 57 find the number ​

Answer 1

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Let the three consecutive odd numbers be :

x , x + 2 , x + 4

According to the statement :-

x + x + 2 + x + 4 = 54

x + x + x = 57 - 2 - 4

3x = 51

x = 51/3

× = 17

So, the three consecutive odd numbers are 17 ,19 , 21.

Answer 2

✴Question:-

The sum of three consecutive odd number is 57 find the number.

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✴Solution:-

→Given:-

• Sum of the numbers = 57

→To find:-

• Actual Numbers (odd)

→Concept:-

• Linear Equation Simple Word Problems.

→Explanation:-

• Here, we will first try to express the three consecutive odd numbers using a single variable n. After this we will equate their sum to 57 to find the value of n and also the values of three consecutive odd numbers.

→Calculation:-

∵We know that any odd number is always of the form (2k+1).We express an odd number in this form because we know that an odd number is not divisible by 2.Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

So, we can say that the difference between any two consecutive odd numbers is:

$= 2k+3–(2k+1)\\=2k+3-2k-1\\=2$

So, for every two consecutive odd numbers there is a difference of 2.

Now, let us take ‘n’ to be an odd number.

So, an odd number just before n will be $(n-2).$

And also an odd number just after n will be $(n+2).$

∵It is given that the sum of these three consecutive odd numbers is 57. So, we can write the following equation:

$n-2+n+n+2=57\\3n=57\\So, n = 19$

The odd number before n will be = $n -2 = 19-2 = 17$

And the odd number after n will be $= n+2 = 19 + 2 = 21$

∴The required three consecutive odd numbers are 17, 19 and 21.

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✴Final Answer:-

The required three consecutive odd numbers are 17, 19 and 21.

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