SOLUTION: I am trying to help my son, but since it's been over 25 years since I took algebra, I'm struggling. I'm not giving him answers. I try to work the problems first to make sure I ca

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Question 845116: I am trying to help my son, but since it's been over 25 years since I took algebra, I'm struggling.
I'm not giving him answers. I try to work the problems first to make sure I can guide him through the process. Here's the question I'm working on. The projected cost of a new high school is $20,066,340, of which $5,216,340 will be covered by available grants. Using data from the last census, the planning committee estimated the cost per town resident. However, new census data reveals that the population has increased by 2200 people, reducing the cost per town resident by $75. What is the current population of the town? (I know that $20,066,340-5,216,340=
$14,850,000; and that amount divided by the population would give me the per resident cost. I also know that this is an inverse variation situation. I just cannot find enough info in the book to guide me through this. I want to answer, "The current population is 2200 more than the previous census showed."). Thank you.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi

let x be the previous population

  |Multiplying thru by x(x+2200) so as all denominators = 1

   14850000(x+2200) = 14850000x + 75x(x+2200)

   75x^2 + 75*2200x - 14850000*2200 = 0

     x^2 + 2200x - 198000*2200 = 0

   x^2 + 2200x  -435600000= 0





    x = 19,800 (Tossing out the negative solution for unit measure)

Population now is : 22,000

CHECKING our answer***

  $750 = $675 + $75



 

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