Question

in a small town, 10 residents move to new cities each year for 3 years. the equation below is written to represent the situation: (-10)·3 = -30 which description best explains the meaning of -30 in the equation? a -30 residents leave the town. b there are -30 residents in the town. c the change in the number of residents per year is -30. d the total change in the number of residents in the town due to people moving away is -30.

Explanation:

Step1: Analyze the meaning of each part of the equation

The \(-10\) represents the number of residents leaving per year (negative because it's a decrease). The \(3\) represents the number of years. When we multiply \(-10\times3=-30\), this is the total change over \(3\) years.

Step2: Evaluate each option

• Option A: It's not \(-30\) residents leaving at once. The equation is a total over 3 years.
• Option B: The number of residents can't be negative in a real - world sense like this.
• Option C: The change per year is \(-10\), not \(-30\).
• Option D: Since \(10\) residents leave each year for \(3\) years, the total change (decrease) in the number of residents due to moving away is \(-30\).

Answer:

D. The total change in the number of residents in the town due to people moving away is \(-30\).