The area of a circle with radius $r$ is given by $\pi r^2$,
and the circumference is given by $2\pi r$.
We are given that the sum of the area and circumference is equal to $80\pi$,
so we can write the equation $\pi r^2 + 2\pi r = 80\pi$.
Dividing both sides by $\pi$, we get $r^2 + 2r = 80$.
Rearranging the terms, we have $r^2 + 2r - 80 = 0$.
This is a quadratic equation, and we can factor it as $(r-8)(r+10) = 0$.
So, the possible values for $r$ are $8$ and $-10$.
Since the radius cannot be negative, the radius of the circle is $\boxed{8}$ units.The answer is: 8
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The area of a circle is represented by x square units, and its circumference is y units. The sum of x and y is equal to 80π. What is the radius of the circle, in units?

### Answer:
