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?

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.