Quadratic Equations, word problem need help please

Question

The captain of a river boat cruise charges $36 per person and gets about 300 customers per day. For every $2 increase in price the captain loses 10 customers a day. He needs to make $12500 so he knows his equation should be, 11500 = (36 + 2x) (300 - 10x) , where (36 + 2x) is the number of times he increases his $36 price by $2 and (300 - 10x) is the number of times he loses 10 people off his 300 people.

 

a) How many times should he increase the price? -Solve by factoring- 

 

b) How much will he now charge?

 

C) How many people will now take the cruise?

 

I really don't understand this question and what I'm supposed to do. I need it done but cannot comprehend what steps to take :(

Answer 1

$36 x 300 per day = $10,800 per day total revenue

$38 x 290 = 11,020 total

39x 285 = 11,115

40 x 280 = 11,200

41 x 275 = 11,275

42 x 270 = 11,340

44x260= 11,440

46x250=11,500

48x240= 11,520

50x 230= 11,500

max is 11,520. he can't make 12,500

(36+2x)(300-10x) = 11,500

2(10)(18+x)(30-x) = 11500

(18+x)(30-x) = 575

-x^2 +12x +540 = 575

x^2-12x +35 = 0

(x-7)(x-5) = 0

x = 5 or 7

36+10 =46 x 250 = 11,500

or 36+14 = 50 x 230 = 11,500