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.

Question

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

(2 points)
Responses

6:8
6:8

9:12
9:12

4:5
4:5

5:6

Answer 1

To determine which ratios are equivalent to the ratio of 3 parts silver to 4 parts green (3:4), you can find equivalent ratios by multiplying both parts of the ratio by the same number.

1. 6:8

   • This can be derived from multiplying both parts of 3:4 by 2:
     \(3 \times 2 = 6\) and \(4 \times 2 = 8\)
   • So, \(3:4\) is equivalent to \(6:8\).

2. 9:12

   • This can be derived from multiplying both parts of 3:4 by 3:
     \(3 \times 3 = 9\) and \(4 \times 3 = 12\)
   • So, \(3:4\) is equivalent to \(9:12\).

3. 4:5

   • This does not match as you cannot simplify \(3:4\) to get \(4:5\).

4. 5:6

   • This does not match as well as it does not maintain the same proportion as \(3:4\).

The two equivalent ratios are:

• 6:8
• 9:12