Tricky quadratic equation question??

Question

ok i need to know how to do this most of all, but the answer also...

A company determines that it can sell 100 calculators per month if the selling price is $25. For each $2 decrease in the price, the number of calculators sold per month increases by 20. Find the revenue function and determine the price the company should sell the calculators for if they want revenue of $3000 for the month..

Thanks a whole bunch

Answer 1

a = amount of change

3000 = (100 + a * 20) * (25 - a * 2)

3000 = 2500 - 200a + 500a -40a^2 | -3000

0 = -40a^2 + 300a - 500 | : (-40)

0 = a^2 -7,5a + 12,5

a1/2 = - (-7,5)/2 +- sqrt( ((-7,5)/2)^2 -12,5)

a1/2 = 3,75 +- 1,25

a1 = 3,75 + 1,25 = 5

a2 = 3,75 - 1,25 = 2,5

=> decreasing the price for calculator by 5*2 = 10 $ or 2,5 * 2 = 5 $ will produce a revenue of 3000 $