Question

The sum of three consecutive numbers is 72 . What are the smallest of these numbers ?

Answer 1

Hint: In this question, we need to find the smallest of the sum of three consecutive numbers. Also given that the sum of three consecutive numbers is \[72\] . The word sum stands for addition . The Consecutive numbers are the numbers following each other continuously. We can start by assuming \[x\] to be the smallest number . Since it is a consecutive number, the second number will be \[x + 1\] and the third number will be \[x + 2\] . Then we need to form an expression as per the question. We need to solve the obtained equation to find the value of \[x\] .

Complete step-by-step answer:
Let us consider the smallest number to be \[x\] and the next numbers can be \[(x + 1)\] and \[(x + 2)\] . Since it is a consecutive number.
Given that the sum of three consecutive numbers is \[72\] .
We need to add the three numbers which are equal to \[72\] .
\[\Rightarrow \ x + (x + 1)\ + (x + 2)\ = 72\]
On adding,
We get,
\[\Rightarrow \ 3x + 3 = 72\]
By subtracting \[3\] on both sides,
We get,
\[\Rightarrow \ 3x + 3 – 3 = 72 – 3\]
On simplifying,
We get,
\[\Rightarrow \ 3x = 69\]
On dividing both sides by \[3\] ,
We get,
\[\dfrac{3x}{3} = \dfrac{69}{3}\]
On simplifying,
We get,
\[\Rightarrow \ x = 23\]
Thus we get the first term, \[x = 23\]
The second term,
\[(x + 1)\ = (23 + 1)\]
On adding,
We get the second term as \[24\] .
The third term,
\[(x + 2)\ = (23 + 2)\]
On adding,
We get the third term as \[25\]
Thus the smallest number is \[23\]
Final answer :
The smallest number is \[23\]

Note: This problem is related to a linear equation with one variable which can be solved by isolating the variable on one side of the equation by performing transformations on the equation . The concept used in this question is consecutive numbers. We should be careful while assuming the consecutive numbers according to the given conditions. If the first term is known then the other terms can be found easily. We can also find the other terms with the formula of the term \[n^{th}\] of an A.P.