Question

If the sum of four consecutive odd integers is $200$, what is the value of first odd integer?
$A)45$
$B)46$
$C)47$
$D)48$

Answer 1

Hint: First, from the given which is the general linear problem of the equations in the one variable. It will be approached by assuming the first number as any of the variables and then successive odd numbers by adding with the number $2$ . from the equation we add the four odd numbers assumed and equate their sum to the given number $200$.

Complete step-by-step solution:
Now we are going to assume the first odd integer as any variable like we take $x$ to be the first odd number. Thus, the consecutive numbers of the odd will be added by the number $2$ because $1,3,5,7,,,,$ the difference is clearly two.
Hence the other odd integers are expressed as $x + 2,x + 4,x + 6$
Since given that the sum of the four numbers is $200$
Thus, which will be expressed mathematically as $x + (x + 2) + (x + 4) + (x + 6) = 200$
Now soling using the addition operation we have $4x + 12 = 200$ and now subtracting the terms using the subtraction operation then we have $4x = 188$
Then by the division operation, we have $4x = 188 \Rightarrow x = \dfrac{{188}}{4} \Rightarrow x = 47$
Hence the value of the first odd integer is $47$ because we assumed the first odd integer as $x$
Therefore, the option $C)47$ is correct.

Note: Since the second odd integer in the above problem can be founded $49$ because the second odd integer can be expressed as $x + 2$
The third odd integer in the above problem can be founded $51$ because the third odd integer can be expressed as $x + 4$
Since the fourth odd integer in the above problem can be founded $53$ because the fourth odd integer can be expressed as $x + 6$
We found the others using the first value of $C)47$
Sometimes students are stuck in selecting the general form of odd and even numbers, we know that in our number system odd and even are alternate. So b/w two successive odd and even numbers the difference is always 2 Hence we have to select in +2 successive order.