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. \(15\) is the number of new residents moving in each year, \(- 3\) is the number of residents moving out each year (since \(3\) move away, it's a negative change). The sum \(15+(-3)\) gives the net change per year. Then multiplying by \(5\) (the number of years) gives the total net change over 5 years.

Step2: Evaluate each option

• Option A: The per - year net change is \(15+( - 3)=12\), not \(60\). So A is wrong.
• Option B: The calculation \(5(15+( - 3))\) is about net gain (since \(15>3\)), not net loss. So B is wrong.
• Option C: \(5(15+( - 3))=5\times12 = 60\). This means after 5 years, the net number of new residents (because \(15\) move in and \(3\) move out each year) is \(60\).
• Option D: The expression is about net change, not the total number of people who move in and then out. So D is wrong.

Answer:

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