Question

Find two consecutive integers whose sum is 68.

Answer 1

Hint:In the given question we are given a sum of two consecutive integers and we are asked to find out those two integers. Consecutive integers follow an order where each succeeding number is one more than the previous number. Example, if x is an integer then, x+1 and x+2 are the two consecutive integers.

Complete step by step answer:
Before dwelling into the problem we should understand what integers are and what consecutive integers are.An integer is any number which is not in decimal or in fraction. An integer includes negative and positive numbers as well as zero.
Example: Decimal as well as fractions are not considered as integers however \[2.00\] and \[\dfrac{3}{3}\] can be classified as integers as they can be simplified into non decimal and non-fraction numbers.Consecutive integers are numbers that follow each other in sequence. There is a difference of 1 between every two subsequent numbers. In a set of consecutive integers, the mean and median are equal.

Now, talking about the given question.Let us assume the two consecutive integers are,\[x\] and \[(x + 1)\]
Therefore,
\[ \Rightarrow x + x + 1 = 68\]
\[ \Rightarrow 2x + 1 = 68\]
\[ \Rightarrow 2x = 68 - 1\]
Thus,
\[ \Rightarrow 2x = 67\]
Therefore,
\[ \Rightarrow x = \dfrac{{67}}{2} = 33.5\]
Thus,
\[ \Rightarrow 33.5 + 1 = 34.5\]
\[ \Rightarrow 33.5 + 34.5 = 68\]

As \[33.5\] and \[34.5\] are not integers. Therefore, 68 cannot be expressed as the sum of two consecutive integers.

Note: In general, when the nature of the integers is not specified we assume the integers in the difference of 1 like we did in the above question, but when the nature is specified as the integers are either consecutive odd or even integers then we shall assume them to be\[x,(x + 2)and (x + 4)\], in order to maintain difference of 2.