Question

Find two consecutive positive odd integers whose sum is $76$

Answer 1

Hint
To answer this question, we have to assume the two numbers in the form of two variables. Then, according to the two conditions given in the question, we have to form two equations. Solving these two equations will give the values of the two variables.

Complete step by step answer
Let the first integer be $x$ and the second integer be $y$
According to the question, these are the consecutive odd numbers. We know that two consecutive odd numbers differ by $2$, therefore we have
$\Rightarrow y - x = 2$ (1)
Also, it is given in the question that the sum of these two numbers is equal to $76$. Therefore, we have
$\Rightarrow x + y = 76$ (2)
From (1) we have
$\Rightarrow y - x = 2$
Adding $x$on both the sides, we get
$\Rightarrow y = x + 2$ (3)
From (2) we have
$\Rightarrow x + y = 76$
Substituting (3) in the above equation, we have
$\Rightarrow x + (x + 2) = 76$
$\Rightarrow 2x + 2 = 76$
Subtracting $2$ from both the sides, we have
$\Rightarrow 2x + 2 - 2 = 76 - 2$
$\Rightarrow 2x = 74$
Dividing by $2$ on both the sides, we get
$\Rightarrow x = 37$
From (3) we have
$\Rightarrow y = x + 2$
Substituting $x = 37$ in this, we have
$\Rightarrow y = 37 + 2$
Finally, we get
$\Rightarrow y = 39$
So, we have $x = 37$ and $y = 39$
Hence, the two consecutive positive odd integers whose sum is $76$, are $37$ and $39$.

Note
In these types of questions involving linear equations, we need to exploit the given information to form the linear equations. The information may not be directly given in the mathematical form in the question. It can be represented just by a phrase in the question statement. For example, in this question the phrase “consecutive positive odd integers” is the information. It is not directly indicated in this question that it can be exploited to form an equation. So read each and every word of the question very much carefully to exploit the full information.