If the ratio of the number of small dogs to the number of large dogs at the animal shelter is 9 to 5. Which of the following is the possible number of small dogs and large dogs at the animal shelter?

The given ratio of small dogs to large dogs is \(9:5\). This means for every 9 small dogs, there are 5 large dogs.

To find possible numbers of small and large dogs at the animal shelter, the total number of each type of dog must be proportional to this ratio. In other words, the number of small dogs and large dogs must be multiples of 9 and 5, respectively.

Let the number of small dogs be \(9x\) and the number of large dogs be \(5x\), where \(x\) is some positive integer.

Thus, any combination of small and large dogs must follow the form:

\[
(9x, 5x)
\]

Now, let's look at some possible numbers of small and large dogs at the shelter:

1. If \(x = 1\), the number of small dogs is 9, and the number of large dogs is 5.
2. If \(x = 2\), the number of small dogs is 18, and the number of large dogs is 10.
3. If \(x = 3\), the number of small dogs is 27, and the number of large dogs is 15.
4. If \(x = 4\), the number of small dogs is 36, and the number of large dogs is 20.
5. If \(x = 5\), the number of small dogs is 45, and the number of large dogs is 25.

So, any combination of small and large dogs must fit these multiples of 9 and 5.

Would you like more details or have any questions? 

Here are five related questions to expand on this concept:
1. If the shelter has 36 small dogs, how many large dogs are there?
2. What is the total number of dogs if there are 54 small dogs?
3. If there are 40 large dogs, how many small dogs should be at the shelter?
4. Can you determine how many small dogs there are if the total number of dogs is 70?
5. What happens to the ratio if we increase the number of large dogs by 50%?

**Tip:** When dealing with ratios, always look for proportional relationships or multiples to solve for unknown values!

Explore how to determine the possible number of small and large dogs at an animal shelter using the given ratio of 9 to 5. This problem focuses on understanding ratios, proportional relationships, and multiples. Ideal for students in Grades 6-8.

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