Question

Sum of three consecutive numbers is 39. Find the numbers.

Answer 1

Hint: Here we will assume the three consecutive numbers as a, a+1 and a+2 and then add them and equate it equal to 39 to evaluate the value of a and then finally find the values of the consecutive numbers.

Complete step by step answer:
Let the three consecutive numbers be $a, a+1$ and $a+2$.
Now it is given that the sum of these consecutive numbers is 39.
Hence, adding them and equating it to 39 we get:-
\[\Rightarrow a + a + 1 + a + 2 = 39\]
Simplifying it we get:-
\[\Rightarrow 3a + 3 = 39\]
Solving it further we get:-
\[\Rightarrow 3a = 36\]
Now solving for the value of a we get:-
\[\Rightarrow a = \dfrac{{36}}{3}\]
On dividing we get:-
\[\Rightarrow a = 12\]
Hence, the first number is 12.
Now putting the value of a in other two numbers we get:-
\[\Rightarrow a + 1 = 12 + 1\]
Simplifying it we get:-
\[\Rightarrow a + 1 = 13\]
Hence, the second number is 13.
Now putting the value of a in the third number we get:-
\[\Rightarrow a + 2 = 12 + 2\]
Simplifying it we get:-
\[\Rightarrow a + 2 = 14\]
Hence, the third number is 14.

Therefore, the three consecutive numbers are 12, 13 and 14.

Note:
Students should note that consecutive numbers are the numbers which have a difference of 1 between them.
Students can also take the consecutive numbers in decreasing order as:-
$a-2, a-1$, and $a$ and then find the numbers.
Now it is given that the sum of these consecutive numbers is 39.
Hence,
\[a + a - 1 + a - 2 = 39\]
Simplifying it we get:-
\[\Rightarrow 3a - 3 = 39\]
Evaluating the value of a we get:-
\[\Rightarrow 3a = 42\]
Solving it further we get:-
\[\Rightarrow a = 14\]
Now putting in the value of a in other two numbers we get:-
\[\Rightarrow a - 1 = 13\]
\[\Rightarrow a - 2 = 12\]

Hence we get the numbers as 12, 13 and 14.