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

The expression \(5(15 + (- 3))\) represents the net change in the number of residents over 5 years. Here, \(15\) is the number of new residents moving in each year and \(-3\) is the number of residents moving out each year. The sum \(15+(-3)\) gives the net increase in the number of residents per year.

Step2: Calculate the net increase per year

\(15+(-3)=15 - 3=12\). This means that each year, there is a net increase of 12 residents.

Step3: Calculate the total change over 5 years

When we multiply the net increase per year (\(12\)) by the number of years (\(5\)), we get \(5\times12 = 60\). This \(60\) represents the total net increase in the number of residents over 5 years. So, after five years, there are 60 new residents in a suburb.

Option A is incorrect because \(15\) is the number of new residents moving in each year, not \(60\). Option B is wrong as the expression calculates the net increase (not the number of residents moving out). Option D is incorrect because the expression is about the net change (not the total number of residents who first moved in and then moved out).

Answer:

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