Meg mixes 3 parts silver paint with 4 parts green paint to get a specific color.

To determine if the ratios 5:6 and 3:4 are equivalent, we can compare them by finding a common method of comparison, which can be done by cross-multiplying.

For the ratio 3:4,

• In fractional form: \( \frac{3}{4} = 0.75 \)

For the ratio 5:6,

• In fractional form: \( \frac{5}{6} \approx 0.8333 \)

Since \( 0.75 \neq 0.8333 \), the two ratios are not equivalent.

Now, let's analyze the responses:

1. "Yes, because both ratios show a pair of numbers that have a difference of 1." - This statement is incorrect because the difference alone does not determine equivalence.

2. "No, because there cannot be more than 4 green parts." - This statement is not relevant to the concept of equivalence of ratios.

3. "No, because the numbers in the given ratio must be multiplied by the same number." - This is a more accurate explanation, although it's not explicitly an accurate mathematical comparison; it implies a misunderstanding of the terms of ratio equivalence.

4. "Yes, because any combination of silver and green will work." - This is not correct, as it misinterprets the meaning of equivalent ratios.

The best option is the one that demonstrates that the two ratios are not equivalent based on a numerical analysis method, which aligns closest to the third response despite its phrasing.

So the answer is No, because the numbers in the given ratio must be multiplied by the same number.