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.
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 A
B.
only factory B
C.
neither factory A nor factory B
D.
both factory A and factory B
To determine if there is a proportional relationship between the number of sandwiches packed and the time spent packaging, we need to check if the ratios of sandwiches packed to time spent are the same for each production line in both factories.
For Factory A:
Line 1: 1800/90 = 20 sandwiches per minute
Line 2: 2400/120 = 20 sandwiches per minute
Line 3: 3000/150 = 20 sandwiches per minute
For Factory B:
Line 1: 2100/105 = 20 sandwiches per minute
Line 2: 2625/125 = 21 sandwiches per minute (not proportional to Line 1)
Line 3: 3190/145 = 22 sandwiches per minute (not proportional to Line 1)
Based on the calculations, we can see that only Factory A has a proportional relationship between the number of sandwiches packed and the time spent packaging. Therefore, the correct answer is:
A. only factory A