Logan and Lily mix blue and red paint to make batches of purple paint as shown in the tables.

Question

2 tables. The first table is a 2-column table with 4 rows titled Logan. Column 1 is labeled Blue with entries 3, 4, 5, 6. Column 2 is labeled Red with entries 9, 12, 15, 18. The second table is a 2-column table with 4 rows labeled Lily. Column 1 is labeled blue with entries 4, 6, 12, 14. Column 2 is labeled Red with entries 10, 15, 30, 35.

Compare the ratios of blue paint to red paint. Which statement is true?
Logan has a higher ratio than Lily.
Lily has a higher ratio than Logan.
Only some of Logan’s ratios are greater than Lily’s ratios.
Logan and Lily’s ratios are equal.

Answer 1

To compare the ratios of blue paint to red paint for both Logan and Lily, we'll calculate the ratios for each entry in the tables.

For Logan:

1. For 3 blue and 9 red: \( \text{Ratio} = \frac{3}{9} = \frac{1}{3} \)
2. For 4 blue and 12 red: \( \text{Ratio} = \frac{4}{12} = \frac{1}{3} \)
3. For 5 blue and 15 red: \( \text{Ratio} = \frac{5}{15} = \frac{1}{3} \)
4. For 6 blue and 18 red: \( \text{Ratio} = \frac{6}{18} = \frac{1}{3} \)

The ratios of blue to red for Logan are all \( \frac{1}{3} \).

For Lily:

1. For 4 blue and 10 red: \( \text{Ratio} = \frac{4}{10} = \frac{2}{5} \)
2. For 6 blue and 15 red: \( \text{Ratio} = \frac{6}{15} = \frac{2}{5} \)
3. For 12 blue and 30 red: \( \text{Ratio} = \frac{12}{30} = \frac{2}{5} \)
4. For 14 blue and 35 red: \( \text{Ratio} = \frac{14}{35} = \frac{2}{5} \)

The ratios of blue to red for Lily are all \( \frac{2}{5} \).

Comparison of Ratios:

• Logan's ratio: \( \frac{1}{3} \) (approximately 0.33)
• Lily's ratio: \( \frac{2}{5} \) (which is 0.4)

Since \( \frac{2}{5} > \frac{1}{3} \), it follows that:

Lily has a higher ratio than Logan.

Therefore, the correct statement is: Lily has a higher ratio than Logan.