To find the largest of four consecutive even integers with an average of 27, let's denote the integers as follows:
- First integer: \(x\)
- Second integer: \(x + 2\)
- Third integer: \(x + 4\)
- Fourth integer: \(x + 6\)
Since the average of these integers is 27, we can write:
| \[ \frac{x + (x + 2) + (x + 4) + (x + 6)}{4} = 27 \] |
Let's simplify the equation:
| \[ \frac{4x + 12}{4} = 27 \] |
Multiplying both sides by 4 gives:
| \[ 4x + 12 = 108 \] |
Subtracting 12 from both sides, we have:
| \[ 4x = 96 \] |
Dividing both sides by 4 to find \(x\):
| \[ x = 24 \] |
The integers are therefore 24, 26, 28, and 30. Hence, the largest integer is 30.
The correct answer is \(30\).
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