https://file.aiquickdraw.com/mathbot/file/1730334298018etiim6eo.jpg

Let's examine and solve this question step-by-step.

### Problem Analysis
The problem gives us the ratio of cats to dogs at different pet stores and asks us to find an equivalent ratio for a new store, "Pet Boutique," based on Pet Smart's ratio.

From the table:
- **Pet Smart** has:
  - Cats: 2
  - Dogs: 14

This gives a ratio of **Cats : Dogs = 2 : 14**. Simplifying this ratio:
\[
\frac{2}{14} = \frac{1}{7} \Rightarrow 1 : 7
\]

Thus, at Pet Smart, for every 1 cat, there are 7 dogs.

### Question
We need to find which option for Pet Boutique matches this **1 : 7** ratio.

### Evaluating Each Option
1. **Option A: 6 cats for every 12 dogs**
   - Ratio: \( \frac{6}{12} = \frac{1}{2} \Rightarrow 1 : 2 \) (Not equivalent to 1 : 7)

2. **Option B: 4 cats for every 20 dogs**
   - Ratio: \( \frac{4}{20} = \frac{1}{5} \Rightarrow 1 : 5 \) (Not equivalent to 1 : 7)

3. **Option C: 7 cats for every 21 dogs**
   - Ratio: \( \frac{7}{21} = \frac{1}{3} \Rightarrow 1 : 3 \) (Not equivalent to 1 : 7)

4. **Option D: 5 cats for every 35 dogs**
   - Ratio: \( \frac{5}{35} = \frac{1}{7} \Rightarrow 1 : 7 \) (Equivalent to 1 : 7)

### Conclusion
The correct answer is **Option D: 5 cats for every 35 dogs**, as it matches the ratio of 1 : 7 found in Pet Smart's data.

Would you like further details on this solution, or have any additional questions?

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### Related Questions
1. How do you simplify a ratio to its lowest terms?
2. What is the method for determining if two ratios are equivalent?
3. How can ratios be represented as fractions for easier comparison?
4. In what real-life situations might ratio equivalence be important?
5. How does cross-multiplication help in comparing ratios?

### Tip
When comparing ratios, it’s often easier to reduce each to its simplest form. This helps quickly identify if two ratios are equivalent.

A new Pet Store, Pet Boutique, has a ratio of Cats to Dogs that is equivalent to Pet Smart. Which of these could be the data for Pet Boutique?
A. 6 cats for every 12 dogs
B. 4 cats for every 20 dogs
C. 7 cats for every 21 dogs
D. 5 cats for every 35 dogs

Solve the problem of finding an equivalent ratio of cats to dogs for a pet store based on Pet Smart's ratio. Learn how to simplify ratios and identify equivalent ones with detailed steps and examples. Ideal for middle school students in grades 6-8.

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