Awine maker has 2 wine barrels labeled a and b. there is more wine in barrel a than in barrel b. the wine maker wants the 2 barrels to contain the exact same amount of wine. to accomplish this, he first pours wine from barrel a into b as much wine as barrel b originally contained. next, he pours from barrel b back into barrel a as much wine as barrel a now contains. finally, he pours back from barrel a into barrel b as much wine as barrel b now contains. at this point the wine maker has accomplished his goal: both barrels contain 48 pints of wine. how much wine did each barrel contain at the very start?

Step-by-step explanation:

Gonna take this nice and slow.  First, at the end it says together both barrels have 48 pints when equal, which means added together they have 96.  This stays even as we  pout from one to the other.  So A+B = 96.  Keep that in mind.  Also I hope you're good with your systems of equations.

One step at a time.  We start with A and B

First, he doubles what is in B, which means he takes that much out of A.

A turns to A-B and B turns to 2B, hopefully you understand that.

Second A is doubled, which means that much is taken out of B.

A-B turns to 2(A-B) or 2A - 2B and 2B turns to 2B - (A - B) or 3B - A

Third and finally B is doubled again

2A - 2B turns to 2A - 2B - (3B - A) or 3A - 5B and 3B - A turns to 2(3B - A) or 6B - 2A

Now we have our system.

A + B = 96

3A - 5B = 6B - 2A or to make it a little nicer 5A = 11B

Let me know if you need help witht he system solving, but you wind up with

A = 66

B = 30

Again, let me know if you don't understand some part.

A=66.   B=30

66-30=36.         30+30=60

36+36=72.          60-36=24

72-24=48.           24+24=48

I divided 96 into 3 pourings  96/3 = 32

64=32=96

But 64 is double than 32,so is a no ending back an forth

66+30= 96 and 66 is more than double than 30

c. (3,2,6) is the answer.