Nonlinear Systems problem, can't quite figure it out!

Question

1. A skateboard company's monthly sales income can be modeled by the equation C(s)=0.5s^2+25s+500, where S represents the number of skateboards sold. The monthly cost of running the business is C(S)=25s+812.5. How many skateboards must the company sell in a month before the sales income equals or exceeds the cost of running the business?

 

2. The deer population in a park can be modeled by the equation P(y)=4y^2-10y+60 where y is the number of years after 2010. The deer population can be modeled by P(y)=10y+80, where y is the number of years after 2010. In which year will the two parks have approximately the same number of deer? 

Answer 1

1)   Income ≥  cost of running

 

     .5s² + 25s + 500 ≥ 25s + 812.5

 

Multiply all terms by 10 to clear the decimal

 

   5s² + 250s + 5000 ≥ 250s + 8125

 

                         5s² ≥ 3125

 

                          s² ≥ 625

 

                           s ≥ 25

 

You must sell 25 skateboards to break even.

 

 

2)  4y² - 10y + 60 = 10y + 80

 

     4y² - 20y  - 20 = 0

 

     4 (y² - 5y - 5) = 0

 

You need to use the Quadratic Formula to solve for y.