Question

Sum of three consecutive integers is 18. Find the numbers.

Answer 1

Hint: Assume any one of the one integer and write the other two using the condition that they are consecutive. Hence use the sum of the integers given to find the three consecutive integers.

Complete step-by-step answer:
An integer is a number that can be written without a fractional component.
Given the problem, we have three consecutive integers.
Sum of these integers is 18.
We need to find these integers.
In order to find these integers, we have to assume any one of the integers.
Let the smallest integer be $x$.
Since the integers are consecutive, the other two integers would be $x+1$ and $x+2$ respectively.
It is given in the problem that the sum of these integers is equal to 18.
$$\begin{gathered} \Rightarrow x+x+1+x+2=18 \\ \Rightarrow 3x=15 \end{gathered}$$
Dividing both side of the above equation by 3, we get
$\Rightarrow x=5$
Hence the three integers are
$$\begin{gathered} x=5 \\ x+1=6 \\ x+2=7 \end{gathered}$$
Therefore, the consecutive numbers are 5,6 and 7.

Alternatively, we can assume the middle integer to be as $x$.
Then the integers would be $x-1,x$and $x+1$.
Using the sum condition, we get
$$\begin{gathered} \Rightarrow x-1+x+x+1=18 \\ \Rightarrow 3x=18 \\ \Rightarrow x=6 \end{gathered}$$
Hence the numbers are
$$\begin{gathered} x-1=5 \\ x=6 \\ x+1=7 \end{gathered}$$
Therefore, the consecutive numbers are 5,6 and 7.

Note:Above problem is related to a linear equation in one variable which is solved by isolating the variable on one side of the equation by performing transformations on the equation. Consecutive integers mean integers following each other continuously. The above problem may also be solved assuming the last integer.