A textile company has specific dyeing and drying times for its different cloths. A roll of Cloth A requires 50 minutes of dyeing time and 45 minutes of drying time. A roll of Cloth B requires 55 minutes of dyeing time and 30 minutes of drying time. The production division allocates 2280 minutes of dyeing time and 1740 minutes of drying time for the week. How many rolls of each cloth can be dyed and dried?

9 rolls of cloth A and 44 roles of cloth B

Step-by-step explanation:

Let x represent the number of rolls of cloth A that can be dyed and dried.

Let y represent the number of rolls of cloth B that can be dyed and dried.

A roll of Cloth A requires 50 minutes of dyeing time. A roll of Cloth B requires 55 minutes of dyeing time. The production division allocates 2280 minutes of dyeing time. This means that

50x + 55y = 2880- - - - - - - -1

A roll of Cloth A requires 45 minutes of drying time. A roll of Cloth B requires 30 minutes of drying time. The production division allocates 1740 minutes of drying time. This means that

45x + 30y = 1740- - - - - - - -2

Multiplying equation 1 by 45 and equation 2 by 50, it becomes

2250x + 2475y = 129600

2250x + 1500y = 87000

Subtracting, it becomes

975y = 42600

y = 42600/975

y = 44

Substituting y = 44 into equation 1, it becomes

50x + 55 × 44 = 2880

50x + 2420 = 2880

50x = 2880 - 2420

50x = 460

x = 460/50

x = 9