Final answer:
To find four consecutive even integers whose sum is 320, we can represent the first even integer as x. The next three consecutive even integers can be represented as x+2, x+4, and x+6. By solving the resulting equation, we find that the four consecutive even integers are 77, 79, 81, and 83.
Step-by-step explanation:
To find four consecutive even integers whose sum is 320, we can represent the first even integer as x. The next three consecutive even integers can be represented as x+2, x+4, and x+6.
Now we can write the equation: x + (x+2) + (x+4) + (x+6) = 320.
Simplifying the equation gives us 4x + 12 = 320.
Subtracting 12 from both sides gives us 4x = 308. Dividing both sides by 4 gives us x = 77.
The four consecutive even integers are therefore 77, 79, 81, and 83.