SOLUTION: 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 th

Question 614943: 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 started out with this equation, by subtracting the grant money ($5,216,340) from the projected cost ($20,066,340). The total cost will be $14,850,000.
I know that if I divide that by each resident (p) then I'll get the amount that each resident has to pay. Because I couldn't figure out the formula, I just plugged in numbers until I got a difference of $75. So the original population was 19,800 and they would have had to pay $750. The new population (19,800 + 2,200) would have to pay $675, which is a difference of $75. There's the answer. My question is, what is the actual formula for figuring out this equation without having to do all that guesswork?
Thanks for your help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The projected cost of a new high school is $20,066,340 of which $5,216,340 will be covered by available grants.
That leaves $14850000 to be paid by town residents.
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Let original population (before increase) be "x" people.
Cost per person will be 14850000/x dollars.
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The new population is (x+2200)
New cost per person will be 14850000/(x+2200) dollars
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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?
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Equation: original cost per person - new cost per person = 75 dollars
14850000/x - 14850000/(x+2200) = 75
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Solve for "x":
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cheers,
Stan H.

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