2. At the kennel, the ratio of cats to dogs is $$ 4: 5 $$. There are 27 animals in all. Here is a tape diagram representing this ratio. a. What is the value of each small rectangle? b. How many dogs are at the kennel? c. How many cats are at the kennel? number of cats month, how many days were rainy? Explain your reasoning. If you get stuck, consider using a tape diagram.

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UpStudy AI · Accepted Answer

To solve the problem, we will follow these steps:

1. **Extract known conditions:**
   - The ratio of cats to dogs is $$ 4:5 $$.
   - The total number of animals (cats + dogs) is $$ 27 $$.

2. **Understanding the ratio:**
   - The ratio $$ 4:5 $$ means that for every $$ 4 $$ cats, there are $$ 5 $$ dogs.
   - The total parts in the ratio can be calculated as $$ 4 + 5 = 9 $$ parts.

3. **Finding the value of each part:**
   - Since there are $$ 27 $$ animals in total, we can find the value of each part by dividing the total number of animals by the total parts in the ratio:
   $$
   \text{Value of each part} = \frac{27}{9} = 3
   $$

4. **Calculating the number of cats and dogs:**
   - To find the number of cats, we multiply the number of parts for cats by the value of each part:
   $$
   \text{Number of cats} = 4 \times 3 = 12
   $$
   - To find the number of dogs, we multiply the number of parts for dogs by the value of each part:
   $$
   \text{Number of dogs} = 5 \times 3 = 15
   $$

Now, let's summarize the answers:

a. The value of each small rectangle is $$ 3 $$.

b. The number of dogs at the kennel is $$ 15 $$.

c. The number of cats at the kennel is $$ 12 $$.
a. Each small rectangle is worth 3. b. There are 15 dogs at the kennel. c. There are 12 cats at the kennel.

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