Understanding the Problem
To find three consecutive even numbers whose sum is 270, we start by defining the numbers.
Defining the Numbers
- Let the first even number be represented as "x."
- The second even number will then be "x + 2."
- The third even number will be "x + 4."
Setting Up the Equation
Now, we can express their sum in an equation:
- x + (x + 2) + (x + 4) = 270
Simplifying the Equation
Combine like terms:
- 3x + 6 = 270
Solving for x
1. Subtract 6 from both sides:
- 3x = 270 - 6
- 3x = 264
2. Divide both sides by 3:
- x = 264 / 3
- x = 88
Finding the Consecutive Even Numbers
Now that we have x, we can find the three consecutive even numbers:
- First number: x = 88
- Second number: x + 2 = 90
- Third number: x + 4 = 92
Conclusion
The three consecutive even numbers whose sum is 270 are:
- 88
- 90
- 92
To verify:
- 88 + 90 + 92 = 270
Thus, the solution is confirmed.