Question

How do you find two consecutive odd numbers whose sum is 276?
 (a) Using linear formulas
(b) Using trigonometric identities
(c) Using algebraic properties
(d) None of these

Answer 1

Hint: To start with, we are to find two consecutive odd numbers whose sum is 276. As we are given two odd numbers, we will start by considering the smaller term as 2x – 1 and the greater term as 2x + 1. Now, adding both terms and simplifying we can easily the value of y. Then putting the values, we are getting the needed numbers.

Complete step by step answer:
According to the question, we are to find two consecutive odd numbers whose sum is 276.
To start with, let us consider the smaller term as, 2x - 1.
We are using this form because we are given that the terms are odd.
Then we have the next odd term as, 2x – 1 +2 = 2x + 1.
Now, it is said that the sum of consecutive two terms is 276.
So, 2x – 1 + 2x + 1 = 276.
Adding and subtracting, 4x = 276.
Dividing both sides by 4, we get, $x=\dfrac{276}{4}=69$.
So, we get the smaller odd term as, 2x – 1 = $\left( 2\times 69 \right)-1=138-1=137$.
Thus, the greater odd term is, 2x + 1 = $\left( 2\times 69 \right)+1=138+1=139$.
Hence, we have the two terms as, 137 and 139.

We have our solution as, (c) Using algebraic properties.

Note:
In this problem, we have dealt with two odd numbers and that is why we have considered it as 2x – 1 and 2x + 1. If we were to deal with two even numbers then we had to consider it as 2x and 2x + 2. These are small details which should be remembered while trying to solve these types of problems.