Question

The sum of $3$ consecutive integers is $90$. What are the $3$ integers ?

Answer 1

Hint: Consecutive integers are those integers that follow each other. They follow a sequence or order. Three consecutive integers means three integers that follow each other like $4,\,5,\,6$. So, if we add these up we get $15$ as a sum. So, in question we need to find three consecutive integers that follow each other and when we add these integers we will get a sum of $90$.

Complete step by step solution:
In the question we need to find three consecutive integers whose sum is $90$ we will use algebra to find these numbers.
Let’s assume the first integer to be $n$
Since the integers are consecutive
Second integer would be $n + 1$
Third integer would be $n + 2$
When we will add these consecutive integers we have a sum of $90$
Therefore, we can write it as
$(n) + (n + 1) + (n + 2) = 90$
Now to solve for $n$, we first add the integers together and $n$ variables together.
So, the above equation becomes
$ \Rightarrow 3n + 3 = 90$
Shifting $3$ to right side of the equation. We get,
$ \Rightarrow 3n = 90 - 3$
$ \Rightarrow 3n = 87$
$ \Rightarrow n = \dfrac{{87}}{3}$
$ \Rightarrow n = 29$
So, first integer is $n = 29$
Second integer $ = n + 1 = 29 + 1 = 30$
Third integer $ = n + 2 = 29 + 2 = 31$
Therefore, three consecutive integers that add up to $90$ are $29,\,30$ and $31$.

Note:
Consecutive means an unbroken sequence so that consecutive integers follow a sequence where each integer is one more than the previous integer. Any set of $n$ consecutive integers will contain exactly one number divisible by $n$ for example any $4$ integers in row must contain a multiple of $4$, any $15$ consecutive integers will contain a multiple of $15$.