SOLUTION: I am having a terrible time trying to figure out! Please Help!! a textile company has a specific dyeing and drying times for its different cloths. A roll of cloth A requires 75

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Question 426658: I am having a terrible time trying to figure out!
Please Help!!
a textile company has a specific dyeing and drying times for its different cloths. A roll of cloth A requires 75 minutes of dyeing time and 50 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 3340 minutes of dyeing time and 2040 minutes of drying time for the week. How many rolls of each cloth can be dyed and dried?

Found 2 solutions by ewatrrr, htmentor:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
the questions Sets up 2 Equations with 2 unknowns
Let x and y be the number of rolls of cloth A and cloth B respectively
Question states***
75x + 55y = 3340min |dyeing time total
50x + 30y = 2040min |drying time total
x = 24, number of rolls of cloth A
and y = 28, number or rolls of cloth B
CHECKING our Answer***
75*24 + 55*28 = 1800 + 1540 = 3340min

Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website!
Set the problem up like this.
Let x = the number of rolls of cloth A
Let y = the number of rolls of cloth B
For the dyeing, we can write the following equation:
75x + 55y = 3340 (1)
For the drying, we can write the following equation:
50x + 30y = 2040 (2)
Now solve for x and y:
Multiply (2) by 3/2 and subtract from (1)
10y = 280 -> y = 28
Subsitute into (2) -> 50x + 30(28) = 2040 -> x = 24
Ans: 24 rolls of cloth A, 28 rolls of cloth B