To determine which recipe requires the least number of berries per batch, we need to calculate the amount of berries used per batch for both the Berry Cobbler and the Berry Pie.
Berry Cobbler
- For 5 batches: 20 pints of berries
- Berries per batch: \( \frac{20 \text{ pints}}{5 \text{ batches}} = 4 \text{ pints/batch} \)
- For 12 batches: 48 pints of berries
- Berries per batch: \( \frac{48 \text{ pints}}{12 \text{ batches}} = 4 \text{ pints/batch} \)
- For 15 batches: 60 pints of berries
- Berries per batch: \( \frac{60 \text{ pints}}{15 \text{ batches}} = 4 \text{ pints/batch} \)
- For 20 batches: 80 pints of berries
- Berries per batch: \( \frac{80 \text{ pints}}{20 \text{ batches}} = 4 \text{ pints/batch} \)
Average for Berry Cobbler: 4 pints per batch.
Berry Pie
- For 4 batches: 7.0 pints of berries
- Berries per batch: \( \frac{7.0 \text{ pints}}{4 \text{ batches}} = 1.75 \text{ pints/batch} \)
- For 10 batches: 17.5 pints of berries
- Berries per batch: \( \frac{17.5 \text{ pints}}{10 \text{ batches}} = 1.75 \text{ pints/batch} \)
- For 20 batches: 35.0 pints of berries
- Berries per batch: \( \frac{35.0 \text{ pints}}{20 \text{ batches}} = 1.75 \text{ pints/batch} \)
- For 50 batches: 87.5 pints of berries
- Berries per batch: \( \frac{87.5 \text{ pints}}{50 \text{ batches}} = 1.75 \text{ pints/batch} \)
Average for Berry Pie: 1.75 pints per batch.
Comparison
- Berry Cobbler: 4 pints per batch
- Berry Pie: 1.75 pints per batch
Conclusion
Berry pie uses less berries per batch.
Double Batch Calculation
- Double batch of Berry Cobbler: \( 2 \times 4 = 8 \text{ pints} \)
- Double batch of Berry Pie: \( 2 \times 1.75 = 3.5 \text{ pints} \)
Difference in Pints
\( 8 - 3.5 = 4.5 \) pints
Therefore, the final answer is:
Berry pie uses less berries. For a double batch, you would need 4.5 fewer pints of berries than needed for a double batch of berry cobbler.