To determine if there is a proportional relationship between the number of sandwiches packed and the time spent packaging in each factory, we need to check if the ratio of sandwiches packed to time spent is constant for all production lines at each factory.
For Factory A:
Line 1:
- Sandwiches Packed = 1,800
- Time Spent = 90
- Ratio = \( \frac{1800}{90} = 20 \)
Line 2:
- Sandwiches Packed = 2,400
- Time Spent = 120
- Ratio = \( \frac{2400}{120} = 20 \)
Line 3:
- Sandwiches Packed = 3,000
- Time Spent = 150
- Ratio = \( \frac{3000}{150} = 20 \)
All ratios for Factory A are equal to 20, indicating a proportional relationship in Factory A.
For Factory B:
Line 1:
- Sandwiches Packed = 2,100
- Time Spent = 105
- Ratio = \( \frac{2100}{105} = 20 \)
Line 2:
- Sandwiches Packed = 2,625
- Time Spent = 125
- Ratio = \( \frac{2625}{125} = 21 \)
Line 3:
- Sandwiches Packed = 3,190
- Time Spent = 145
- Ratio = \( \frac{3190}{145} = 22 \)
The ratios for Factory B are 20 for Line 1, 21 for Line 2, and 22 for Line 3, which are not constant, indicating that there is no proportional relationship in Factory B.
Conclusion:
There is a proportional relationship only in Factory A. Thus, the correct answer is:
C. only factory A