# algebra

posted by on .

could you please show me how to do this problem?
ballfield costs 14,850,00 to build. the cost per city resident to build it will be based on last census. New census shows population increased by 2200 people, which reduced the cost per resident \$75. what is the current population of the city?? thank you

• algebra - ,

The way you grouped the cost by thousands, I think you left out a zero
is it 14 850 000 ?

let currect population be x
last year's population is x - 2200

currect cost per person = 14850000/x
last year's cost per person = 14850000/(x-2200)

14850000/(x-2200) - 14850000/x = 75
14850000x - 14850000(x-2) = 75x(x-2200)

75x^2 - 165000x - 14850000(2200) = 0
x^2 - 2200x = 435 600 000
x^2 - 2200x + 1210000 = 435 600 000 + 1 210 000
(x - 1100)^2 = 436 810 000
x - 1100 = 20900
x = 22 000

check:
current pop: = 22000
cost per person = 14850000/22000 = 675

last years' pop = 19800
cost per person = 14850000/19800 = 750

change = 750-675 = 75 , YEAHH!

• algebra - ,

yes you were right about the zero. Thank you so much for showing me how to do it. ann