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 \(5(15+(- 3))\) is used. Here, \(15\) is the number of new residents moving in each year and \(-3\) is the number of residents moving away each year (since moving away is a decrease). The sum \(15+(-3)=15 - 3=12\) gives the net number of new residents per year.

Step2: Consider the multiplier

The number \(5\) represents the number of years. When we calculate \(5\times(15 + (-3))=5\times12 = 60\), we are finding the total net number of new residents over \(5\) years.

• Option A: The net new residents per year is \(12\) (not \(60\)), so A is wrong.
• Option B: The calculation is about net new residents (not those moving out), so B is wrong.
• Option D: The expression is about net change (not total in - then - out), so D is wrong.

So, after five years, there are 60 new residents in a suburb (Option C).

Answer:

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