Answered

Magtanong at makakuha ng malinaw na mga sagot sa IDNStudy.com. Makakuha ng mga sagot sa iyong mga tanong mula sa aming mga eksperto, handang magbigay ng mabilis at tiyak na solusyon.

Kurt's father is 2 more than eight times his age. If the product of their ages in years is 300, how old are they?
Show me a solution

Sagot :

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