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 moving away each year (negative because it's a decrease). The $3$ represents the number of years.

Step2: Understand the result of the multiplication

When we multiply $(-10)\times3$, we are finding the total change over 3 years. Since $10$ residents leave each year for 3 years, the total number of residents who have left (total change) is $10\times3 = 30$, and because it's a decrease, it's $-30$.

• Option A is incorrect because it's not that $-30$ residents leave (you can't have a negative number of people leaving in the sense of count, the negative represents a decrease).
• Option B is incorrect because you can't have $-30$ residents (number of people can't be negative in that context).
• Option C is incorrect because the change per year is $-10$, not $-30$.

Answer:

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