Let's start by assigning variables to the ages of Charlie and Ava.
Let x be the age of Ava, then Charlie's age is x + 2 (since their ages are consecutive even integers).
We know that the product of their ages is 80, so we can set up the equation:
x(x + 2) = 80
Expanding the left side:
x^2 + 2x = 80
Subtracting 80 from both sides:
x^2 + 2x - 80 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = 2, and c = -80:
x = (-2 ± sqrt(2^2 - 4(1)(-80))) / 2(1)
Simplifying:
x = (-2 ± sqrt(324)) / 2
x = (-2 ± 18) / 2
x = -10 or x = 8
Since we are looking for a positive age, Ava is 8 years old, and Charlie is x + 2 = 10 years old.
Therefore, Charlie is 10 years old.