Jos is 33 years younger than his father. The product of their ages is 658 . How old is Jos?

Let Jos's age be \( j \). Then, his father's age would be \( j + 33 \). The equation based on their ages can be set up as follows: \[ j(j + 33) = 658 \] Expanding this gives: \[ j^2 + 33j - 658 = 0 \] Now, we can apply the quadratic formula \( j = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 1 \), \( b = 33 \), and \( c = -658 \). Calculating the discriminant: \[ b^2 - 4ac = 33^2 - 4 \cdot 1 \cdot (-658) = 1089 + 2632 = 3721 \] Now we find the square root of 3721, which is 61. Plugging this back into the quadratic formula gives: \[ j = \frac{-33 \pm 61}{2} \] This results in two possible solutions: 1. \( j = \frac{28}{2} = 14 \) 2. \( j = \frac{-94}{2} = -47 \) (not a valid age) Thus, Jos is 14 years old. So the conclusion is: Jos is 14 years old!