In a given year, the population of Metro City is 7420, and the population is decreasing by 152 people per year. The population of Smallville is consistently 1200 less than half of Metro City. Determine how long it will take for Smallville's population to reach 2282.
Which answer provides the correct equation and solution for the situation, where x represents the number of years?
A. The equation is 2282=12(7420−152x)−1200. It will take 3 years for the population of Smallville to be 2282 people.
B. The equation is 2282=2(7420−152x)+1200. It will take 45.26 years for the population of Smallville to be 2282 people.
C. The equation is 2282=2(7420−152x)+1200. It will take 45.26 months for the population of Smallville to be 2282 people.
D. The equation is 2282=12(7420−152x)−1200. It will take 3 months for the population of Smallville to be 2282 people.
i really don't know
p(x) = 7420-152x
s(x) = 1/2 p(x) - 1200 = 3710-76x-1200 = 2510-76x
So, what do you think?
it is A my apologizes it was in the wrong order
To determine how long it will take for Smallville's population to reach 2282, we can start by finding the equation that represents the population of Smallville over time.
Given that the population of Metro City is 7420 and decreasing by 152 people per year, we can express the population of Metro City as: 7420 - 152x, where x represents the number of years.
The population of Smallville is consistently 1200 less than half of Metro City. Therefore, the population of Smallville can be represented as: (1/2) * (7420 - 152x) - 1200.
Now, we can set up the equation and solve for x:
(1/2) * (7420 - 152x) - 1200 = 2282
Multiplying both sides of the equation by 2 to eliminate the fraction:
7420 - 152x - 2400 = 4564
Combine like terms:
5020 - 152x = 4564
Subtracting 5020 from both sides:
-152x = -456
Dividing both sides by -152:
x = 3
This means that it will take 3 years for the population of Smallville to reach 2282 people.
Therefore, the answer choice that provides the correct equation and solution is:
A. The equation is 2282 = 12(7420 - 152x) - 1200. It will take 3 years for the population of Smallville to be 2282 people.