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  • Brainly User
2015-09-03T00:56:20+08:00
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



 

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