Let's denote Rudy's current age as \( x \) years and his son's current age as \( y \) years.
According to the given information:
1. Rudy is now five times as old as his son, so we have the equation \( x = 5y \).
2. Six years ago, the product of their ages was 68, which means \((x-6)(y-6) = 68\).
Substituting the value of \( x \) from the first equation into the second equation, we get:
\((5y-6)(y-6) = 68\)
Expanding this equation, we get:
\(5y^2 - 36y + 36 = 68\)
Now, let's simplify and rearrange to form a quadratic equation:
\(5y^2 - 36y + 36 - 68 = 0\)
\(5y^2 - 36y - 32 = 0\)
So, the quadratic equation formed using Rudy's age as the variable is \(5y^2 - 36y - 32 = 0\).
Now, to find their present ages, we can solve this quadratic equation for \( y \)
