To compare the ratio of sugar to berries for both batches, we need to calculate the ratio for each batch.
For last week's batch:
- Sugar: 2 cups
- Berries: 18 cups
The ratio of sugar to berries is: \[ \text{Ratio}_{\text{last week}} = \frac{\text{sugar}}{\text{berries}} = \frac{2}{18} = \frac{1}{9} \]
For this week's batch:
- Sugar: 4 cups
- Berries: 30 cups
The ratio of sugar to berries is: \[ \text{Ratio}_{\text{this week}} = \frac{\text{sugar}}{\text{berries}} = \frac{4}{30} = \frac{2}{15} \]
Next, we need to compare the two ratios: \(\frac{1}{9}\) and \(\frac{2}{15}\).
To compare \(\frac{1}{9}\) and \(\frac{2}{15}\), we can find a common denominator. The least common multiple of 9 and 15 is 45.
Convert \(\frac{1}{9}\) to a denominator of 45: \[ \frac{1}{9} = \frac{1 \times 5}{9 \times 5} = \frac{5}{45} \]
Convert \(\frac{2}{15}\) to a denominator of 45: \[ \frac{2}{15} = \frac{2 \times 3}{15 \times 3} = \frac{6}{45} \]
Now we can compare \(\frac{5}{45}\) and \(\frac{6}{45}\): \[ \frac{5}{45} < \frac{6}{45} \]
This shows that the ratio of sugar to berries in last week's batch (\(\frac{1}{9}\)) is less than the ratio of sugar to berries in this week's batch (\(\frac{2}{15}\)).
Therefore, this week's batch had a greater ratio of sugar to berries.