Question

in suburbs of large cities,15 new residents move in each year. of those 15, three will move away each year. which of the of the following best describes the meaning of 60, from the expression: $5(15+(-3)) = 60$? a each year 60 new residents move into the suburb. b after five years, 60 new residents have already moved out of a certain suburb. c after five years, there are 60 new residents in a suburb. d over five years, 60 residents first move in, then move out of the suburb.

Explanation:

Step1: Analyze the expression components

In the expression \(5(15 + (-3))\), \(15\) is the number of new residents moving in per year, \(-3\) is the net change (since \(3\) move away, it's like \(+(-3)\)), and \(5\) is the number of years.

Step2: Calculate the annual net change

First, calculate the annual net change: \(15+(-3)=15 - 3=12\). This means that each year, on net, \(12\) new residents stay (after accounting for those who move away).

Step3: Calculate the total over 5 years

Then, multiply the annual net - change by the number of years. Using the expression \(5\times12 = 60\). This \(60\) represents the total number of new residents in the suburb after \(5\) years.

Answer:

C. After five years, there are 60 new residents in a suburb.