Final answer:
To find the weights of metal castings, we can set up a system of equations. The weight of the first casting is 36 lb, and the weight of the second casting is 48 lb.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's say the weight of the first casting is x lb. Then, the weight of the second casting is x + 12 lb. We know that the total weight of both castings is 84 lb. So, we can write the equation: x + (x + 12) = 84
Simplifying the equation, we get 2x + 12 = 84. Subtract 12 from both sides: 2x = 72. Then, divide both sides by 2: x = 36.
Therefore, the weight of the first casting is 36 lb, and the weight of the second casting is 36 + 12 = 48 lb.