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).

Step2: Understand division in context

Dividing by \(3\) (the number of days) gives the average change per day. The negative sign indicates a decrease. So, \(-8\) means an average decrease of \(8\) dogs per day.

Step3: Evaluate options

• Option A: The total decrease is \(24\) (not \(8\)), so A is wrong.
• Option B: There is a decrease (not increase), so B is wrong.
• Option C: Matches the analysis (\(-8\) is average daily decrease), so C is correct.
• Option D: The meaning of \(-8\) is about average daily decrease, not about not having enough dogs in a non - mathematical sense, so D is wrong.

Answer:

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