Let Kurt's age = x
age of Kurt's father = 8x + 2
Product of their ages = 300
Equation:
(x) (8x + 2) = 300
8x² + 2x = 300
Rewrite in standard form (quadratic equation):
8x² + 2x - 300 = 0
Solve by factoring, take out 2 (which is the GCF of all terms.
2 (4x² + x - 150) = 0
2 ( x-6) (4x + 25) = 0
solve for roots (x):
x - 6 = 0 4x + 25 = 0
x = 6 4x = -25
4 4
x = -25
4
Choose the positive solution, x = 6
The ages are:
Kurt's age: x = 6 years old
Father's age = 8x + 2
= 8 (6) + 2
= 48 + 2
= 50 years old.
To check, the product of their ages is 300.
(6) (50) = 300
300 = 300