Question

Find three consecutive even numbers whose sum is 234.

Answer 1

Hint: The three consecutive even numbers differ by two. Use this fact to assign variables to the numbers and find the equation relating to the variable. Solve the equation to find the answer.

Complete step-by-step answer:
We need to find three consecutive even numbers whose sum is 234.
We know that consecutive numbers are nearest neighbors to the number and which occur together.
For consecutive even numbers, they differ by two numbers since every second number is an even number.
Using the above fact, let us assume the three consecutive even numbers to be 2x, 2x + 2, and 2x+4 in the same increasing order.
It is given that the sum of the three consecutive even numbers is 234.
\[2x + 2x + 2 + 2x + 4 = 234\]
Simplifying the above equation, we have:
\[6x + 6 = 234\]
Solving for x from the above equation, we get:
\[6x = 228\]
\[x = \dfrac{{228}}{6}\]
\[x = 38..........(1)\]
Using equation (1), we get the value of the three consecutive even numbers.
We find the value of 2x as follows:
\[2x = 76\]
Now, we find the value of 2x + 2 as follows:
\[2x + 2 = 78\]
Now, we find the value of 2x + 4 as follows:
\[2x + 4 = 80\]
Hence, the three consecutive even numbers are 76, 78, and 80.

Note: We can also choose the three consecutive even numbers as 2x-2, 2x, 2x +2, so that the number 2 cancels out and the sum is simplified. The only necessity is that they need to differ by 2 each and the first term should be an even number.