Final answer:
To find the number of years ago when the product of their ages was 105, we can set up another equation and solve the quadratic equation. The product of their ages was 105 about 6.88 years ago.
Step-by-step explanation:
To solve this problem, we need to set up equations using the information given. Let's assume the present age of the father is x and the present age of the son is y. After 40 years, the father will be x + 40 years old and the son will be y + 40 years old. It is given that x + 40 = 8 and y + 40 = 8. Solving these equations, we get x = -32 and y = -32. However, age cannot be negative, so these values are not valid.
To find the number of years ago when the product of their ages was 105, we can set up another equation. Let's assume z is the number of years ago. So, the father's age z years ago would be x - z and the son's age z years ago would be y - z. The equation to find z would be (x - z)(y - z) = 105.
Plugging in the values of x and y from the previous equations, we get (-32 - z)(-32 - z) = 105. Simplifying this equation, we obtain z^2 + 64z - 1217 = 0. Solving this quadratic equation, we find that z is approximately 6.88 years ago. Therefore, the product of their ages was 105 about 6.88 years ago.