Final answer:
To solve the weight problem, two equations were set up based on the given conditions, and algebra was used to determine that bucket A originally weighed 18 lbs and bucket B weighed 12 lbs.
Step-by-step explanation:
The question requires solving a weight problem using basic algebra. Let's denote the weight of bucket A as A and the weight of bucket B as B. Initially, they weigh 30 lbs together, so we have the equation A + B = 30. After transferring 6 lbs of oil from A to B, we have another equation: A - 6 = B + 6 because the weight of bucket A decreases by 6 lbs, and the weight of bucket B increases by 6 lbs. Since the buckets weigh the same after the transfer, we can equate these expressions to find out the individual weights.
Setting up the equations:
1. A + B = 30 (Initial total weight)
2. A - 6 = B + 6 (Equal weight after transfer)
We can combine these equations to solve for A and B. By subtracting the second equation from the first, 2B = 24, and dividing by 2, we get B = 12. Plugging the value of B into one the first equation, we get A = 30 - B, which gives us A = 18.
Therefore, before transferring the oil, bucket A weighed 18 lbs and bucket B weighed 12 lbs.