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 division operation

We have \(-24\div3=-8\). The total number of dogs adopted out (decrease in population) is \(24\) (represented as \(- 24\) since it's a decrease) over \(3\) days.

Step2: Interpret the result

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

Option A is wrong because \(24\) dogs were adopted out (total decrease is \(24\), not \(8\)). Option B is wrong as there is a decrease (not an increase) in the number of dogs. Option D is an incorrect interpretation of the mathematical operation.

Answer:

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