Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios.

Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check the two that apply.

(2 points)
Responses

5:6
5:6

9:12
9:12

6:8
6:8

4:5

1 answer

To determine which ratios are equivalent to the ratio of 3 parts silver to 4 parts green (which can be expressed as 3:4), we can simplify the ratios given in the responses to see if they match.

  1. 5:6 - This simplifies to 5 parts silver and 6 parts green. To compare, we can cross-multiply: \(5 \times 4 \neq 6 \times 3\). Therefore, this ratio is not equivalent.

  2. 9:12 - This ratio can be simplified by dividing both parts by 3, resulting in 3:4. So, this ratio is equivalent.

  3. 6:8 - This ratio can be simplified by dividing both parts by 2, resulting in 3:4. So, this ratio is also equivalent.

  4. 4:5 - Cross-multiplying gives \(4 \times 4 \neq 5 \times 3\), so this ratio is not equivalent.

Correct answers: 9:12 and 6:8.