SOLUTION: melinda's dad is 30 years older than melinda is now. eight years ago, his age was equal to the square of melinda's age then. how old is melinda now?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: melinda's dad is 30 years older than melinda is now. eight years ago, his age was equal to the square of melinda's age then. how old is melinda now?      Log On


   

Question 130837This question is from textbook
: melinda's dad is 30 years older than melinda is now. eight years ago, his age was equal to the square of melinda's age then. how old is melinda now? This question is from textbook

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Melinda is x years old now.
Dad is x + 30 years old now.
Eight years ago, Dad was x + 30 - 8 = x + 22 years old, and Melinda was x - 8 years old. Melinda's age squared 8 years ago would then be x%5E2-16x%2B64.

x%5E2-16x%2B64=x%2B22

x%5E2-17x%2B42=0

-14%2A-3=42 and -14-3=-17, so:

%28x-3%29%28x-14%29=0. So, Melinda is either 3 years old, or she is 14 years old. But the answer 3 is absurd, because that means her age 8 years ago was -5. So we can exclude that answer as an extraneous root caused by squaring the variable when we set up the problem in the first place. The correct answer is Melinda is 14.

Check:
14 + 30 = 44
14 - 8 = 6, 6 X 6 = 36, and 44 - 8 = 36, answer checks.