Question

Find any two consecutive integers whose sum is$126$?

Answer 1

Consecutive numbers means the pair of numbers, such that the relation of first number to the second is exceeding to the first, or we can say when they go along the number line in series every two numbers taking forward are consecutive numbers.
For example for any number “c” the consecutive number to it is “$c + 1$” .

Complete step by step solution:
Given number is $126$

Let suppose the first consecutive number and the next consecutive number as,
$x\,and\,x + 1$

Now according to question sum of two consecutive number is given that is $126$

Now, form an equation in which put the assumed consecutive numbers in the left and put the given number in right side of equation after equal sign, doing this:
We get the equation as,

$$x\, + (x + 1) = 126 \\\ \Rightarrow 2x + 1 = 126 \\\ \Rightarrow 2x = 126 - 1 \\\ \Rightarrow 2x = 125 \\\ \Rightarrow x = \dfrac{{125}}{2} \\\ \Rightarrow x = 62.5 \\\$$

So the required numbers are
$x = 62.5\,and\,(x + 1) = 62.5 + 1 = 63.5$

Formulae Used: For any number “c” the consecutive number to it is “$c + 1$” .

Additional Information: You have to be sure that the second consecutive number is always one exceeding the first one.

Note: In the above question there was no any other condition in the consecutive numbers but in higher level question you can have certain conditions in your consecutive number like one can ask that the next consecutive number is five time greater than the first one, or they can give you the ratio between the consecutive numbers or their can be any difference given between the consecutive numbers then you have to solve accordingly.