Mr. Wells is comparing data about the packaging of sandwiches at two factories. The table shows the number of sandwiches packed and the time spent packaging for three production lines at two factories during a morning shift.

Question

Factory A Factory B
Production
Line Sandwiches
Packed Time Spent
(minutes) Production
Line Sandwiches
Packed Time Spent
(minutes)
Line 1 1,800 90 Line 1 2,100 105
Line 2 2,400 120 Line 2 2,625 125
Line 3 3,000 150 Line 3 3,190 145

At which factory is there a proportional relationship between the number of sandwiches packed and the time spent packaging?
A.
only factory B
B.
neither factory A nor factory B
C.
only factory A
D.
both factory A and factory B

Answer 1

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