To determine the correct proportion describing the relative amounts of each color of blocks in both groups, we should first find the ratios of red to green blocks for each group.
For the first group:
- Red blocks: 15
- Green blocks: 45
The ratio of red to green blocks is:
\[ \frac{15}{45} = \frac{1}{3} \]
For the second group:
- Red blocks: 30
- Green blocks: 90
The ratio of red to green blocks is:
\[ \frac{30}{90} = \frac{1}{3} \]
Now that we have both ratios as \( \frac{1}{3} \), we can express them as proportions.
Let’s analyze the options given:
- \( \frac{15}{45} = \frac{90}{30} \) → Not correct.
- No response or invalid options.
- \( \frac{1}{3} \) → The correct answer since it reflects the ratio for both groups.
- \( \frac{15}{45} = \frac{30}{90} \) → This is a valid way to express the equivalency of the ratios of the red to green blocks for both groups.
The most appropriate responses that correctly describe the relative amounts of each color are \( \frac{15}{45} = \frac{30}{90} \) or the simplified ratio of \( 1:3 \) for both groups.
Thus, the choice equivalent to \( 15:45 = 30:90 \) is valid.