Answer:
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.
