Question 1064454: .
Will someone please show me the solution to this word problem: 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?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Let x = the estimated population.
x+2200=current population
14,850,000/x is the original cost per resident.
14,850,000/(x+2200) is $75 less.
Therefore, 14,850,000/x -75=14,850,000/(x+2200)
The left side term over a common denominator is (14,850,000-75x)/x=14,850,000/(x+2200)
Cross-multiply
14,850,000x=14,850,000x+32670000000-75x^2-165000x
The 14,850,000x cancel
-75x^2-165000x+32670000000=0
divide both sides by -75
x^2+2200-435,600,000=0
x=(1/2) -2200+/- sqrt (4,840,000+1,742400000); the sqrt term is 41800
x=(1/2) -2200+41,800=19,800
The current population is 22,000
Check: 14,850,000/19800=750
and 14,850,000/22000=675
It checks.
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