Question

In a room with mini and giant dogs, if 5 mini dogs went out and 5 giant dogs came in, there would be just as many mini dogs as giant dogs. However, if 5 giant dogs went out and 5 mini dogs came in, there would be twice as many mini dogs as giant dogs. How many giant dogs were originally in the room?

Answer 1

To solve the problem, we created a system of equations using variables for the number of mini and giant dogs. By applying the given scenarios, we determined there were originally 25 giant dogs in the room.

Step-by-step explanation:

We need to figure out how many giant dogs were originally in the room based on the given conditions. Let's define the number of mini dogs as M and the number of giant dogs as G. Initially, we have no information about the number of mini dogs, but we can write the conditions in terms of M and G.

According to the first scenario, if 5 mini dogs left and 5 giant dogs entered, the number of mini and giant dogs would be equal. So, we can write the first equation as follows: M - 5 = G + 5.

For the second scenario, if 5 giant dogs left and 5 mini dogs entered, there would be twice as many mini dogs as giant dogs, which gives us the second equation: M + 5 = 2(G - 5).

Now, we have a system of equations:

1. M - 5 = G + 5
2. M + 5 = 2(G - 5)

Let's solve the system to find G. From the first equation, we get M = G + 10. Substitute this into the second equation and simplify:

1. G + 10 + 5 = 2(G - 5)
2. G + 15 = 2G - 10
3. 25 = G

So, there were originally 25 giant dogs in the room before any of them went out or came in.