Package A weighs half as much as Package B. Package B weighs four times as much as Package C. The total weight of Package A and Package C is 648 grams. Find the weight of Package B.

a = b/2

b = 4c
a+c = 648

so,

b/2 + b/4 = 648
3/4 b = 648
b = 648 * 4/3 = 864

To solve this problem, we can set up a system of equations to represent the given information. Let's assign variables to represent the weights of the packages:

Let's say the weight of Package C is x grams.

According to the given information:
Package A weighs half as much as Package B, so the weight of Package A would be 0.5 times the weight of Package B, which is 0.5B.
Package B weighs four times as much as Package C, so the weight of Package B would be 4 times the weight of Package C, which is 4x.

The total weight of Package A and Package C is given as 648 grams, so we can write the equation:

0.5B + x = 648

Now, let's solve for B.

Substitute the value of B in terms of x into the equation:

0.5(4x) + x = 648
2x + x = 648
3x = 648
x = 648/3
x = 216

So, the weight of Package C is 216 grams.

Now, substitute the value of x back into the equation to find the weight of Package B:

B = 4x = 4(216) = 864

Therefore, the weight of Package B is 864 grams.