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 meaning

The equation \(-24\div3=-8\) represents the situation of dog adoptions. Here, \(-24\) is the total number of dogs adopted out (a decrease, so negative), and \(3\) is the number of days.

Step2: Interpret the quotient

When we divide the total decrease in the number of dogs (\(-24\)) by the number of days (\(3\)), the result \(-8\) means that, on average, the number of dogs in the shelter decreased by \(8\) each day. The negative sign indicates a decrease.
Option A is wrong because \(-24\) is the total decrease, not \(-8\). Option B is wrong as there is a decrease, not an increase. Option D is an incorrect interpretation of the mathematical meaning of the equation.

Answer:

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