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
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!
yes you were right about the zero. Thank you so much for showing me how to do it. ann
Sure! Let's break down the information given in the problem and find a solution step by step.
1. We are told that the cost of building the ballfield is $14,850,00.
2. The cost per city resident to build the ballfield is based on the last census.
3. The new census shows that the population has increased by 2200 people, which has reduced the cost per resident by $75.
4. We need to find the current population of the city.
To solve this problem, we can set up an equation based on the given information.
Let's assume that the previous population of the city is "P," and the cost per resident based on the last census is "C" dollars.
According to the given information, the previous population and cost per resident relationship is:
Cost per resident = Total cost of building the ballfield / Previous population
C = $14,850,00 / P
Now, with the new census, the cost per resident has reduced by $75 and the population has increased by 2200. Let's update our equation using these changes.
New cost per resident = (Total cost of building the ballfield) / (Previous population + 2200)
(C - 75) = $14,850,00 / (P + 2200)
Now we have two equations:
C = $14,850,00 / P
(C - 75) = $14,850,00 / (P + 2200)
To find the current population, we can solve these equations simultaneously.
1. First, let's solve the equation C = $14,850,00 / P for C:
C = $14,850,00 / P
C * P = $14,850,00
P = $14,850,00 ÷ C
2. Next, substitute this value for P in the second equation:
(C - 75) = $14,850,00 / (P + 2200)
(C - 75) = $14,850,00 / (($14,850,00 ÷ C) + 2200)
Simplifying the equation further, we can cross-multiply and rearrange to solve for C:
C * (C - 75) = $14,850,00 * (C + 2200 - 75)
C^2 - 75C = $14,850,00C + $32,670,00 - $1,110,000
C^2 - $14,937,00C - $1,110,000 + $32,670,00 = 0
C^2 - $14,937,00C + $21,915,00 = 0
Now we have a quadratic equation in terms of C. We can solve this equation using the quadratic formula:
C = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = -14,937,00, and c = $21,915,00.
By using the quadratic formula, you can find two possible values for C, which represent the cost per resident based on the last census.
Once you have these values, substitute them back into the equation P = $14,850,00 ÷ C to find the corresponding two possible populations.
In this way, you can determine the current population of the city.