Question

danika runs an adoption shelter for dogs. she adopts out twenty - four dogs over a three - day weekend to new homes. the following equation is written to represent the situation: $-24div3=-8$. which of the following best explains the meaning of $-8$ in the equation? a the total dog population in the shelter decreased by a total of 8 dogs over the three - day weekend. b the dog population in the shelter increased by an average of 8 dogs each day of the three - day weekend. c the dog population in the shelter decreased by an average of 8 dogs each day of the three - day weekend. d the dog population in the shelter is considered $-8$ because danika did not have enough dogs to adopt out to families over the three - day weekend.

Explanation:

Step1: Analyze the equation

The equation is \(-24\div3=-8\). Here, \(-24\) represents the total decrease in the number of dogs (since dogs are adopted out, the population decreases) over 3 days.

Step2: Interpret the division

When we divide \(-24\) (total decrease) by 3 (number of days), \(\frac{-24}{3}=-8\). The negative sign indicates a decrease. The value 8 is the average amount per day. So, it means the dog population decreased by an average of 8 dogs each day.

• Option A is wrong because \(-8\) is per day, not total over the weekend.
• Option B is wrong because the population is decreasing (negative sign in the equation), not increasing.
• Option D is wrong as the \(-8\) is an average daily decrease, not because of not having enough dogs in a wrong sense as described.

Answer:

C. The dog population in the shelter decreased by an average of 8 dogs each day of the three - day weekend.