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 residents moving in each year and \(-3\) is the number of residents moving out each year. The sum \(15+(-3)\) gives the net number of residents per year. Then multiplying by \(5\) (years) gives the total net change over 5 years.

Step2: Evaluate each option

• Option A: The number of new residents moving in each year is \(15\), not \(60\). So, A is incorrect.
• Option B: The expression calculates the net gain (since \(15>3\)), not the number of residents moving out. So, B is incorrect.
• Option C: Since \(15 + (-3)=12\) (net residents per year) and \(5\times12 = 60\), this represents the total net number of new residents after 5 years.
• Option D: The expression is about net change (not first - in - then - out in a non - net sense). So, D is incorrect.

Answer:

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