Question

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=2(7420−152x)+1200. It will take 45.26 years for the population of Smallville to be 2282 people.

B. The equation is 2282=2(7420−152x)+1200. It will take 45.26 months for the population of Smallville to be 2282 people.

C.The equation is 2282=12(7420−152x)−1200. It will take 3 months for the population of Smallville to be 2282 people.

D. The equation is 2282=12(7420−152x)−1200. It will take 3 years for the population of Smallville to be 2282 people.

Answer 1

The correct option is D.

Explanation:

Let x denote the years.

The information provided is:

• The population of Metro City is 7420.
• The population is decreasing by 152 people per year.
• The population of Smallville is consistently 1200 less than half of Metro City.

From the provided data derive the equation for the population of Smallville x years after as follows:

`Y = [(1)/(2)\cdot (7420-152x)]-1200`

The population of Smallville is 2282 after x years.

Compute the value of x as follows:

`2282= [(1)/(2)\cdot (7420-152x)]-1200`

`(7420-152x)/(2)=2282+1200\\\\7420-152x=3482* 2\\\\152x=7420-6964\\\\152x=456\\\\x=3`

Thus, the time it will take for Smallville's population to reach 2282 is 3 years.

The correct option is D.