I got this question right early in semester but now I am studying it and cannot

Question

I got this question right early in semester but now I am studying it and cannot remember how I got the answer.

Lucas Company uses the weighted-average in its process costing system. The company adds materials at the beginning of the process in the Forming Department, which is the first of two stages in its production process. Information concerning operations in the Forming Department in October follows:

.................................................Units.............Materials Cost
Work in process on October 1..............6,000.............$3,000
Units started during October...............50,000.............$25,560
Units completed and transferred to
the next Department during October.....44,000

What was the materials cost of work in process at October 31?

Correct answer is $6,120....but I cannot remember how I got it...can someone help?

Explanation / Answer

The company started with 6000 wip units in its inventory and it added 50,000 more during the month, giving them a total of 56,000 incomplete units. 44,000 of those were completed by the end of the month, leaving them with 56,000 - 44,000 = 12,000 units left over in the work in process inventory at October 31.

Now using the weighted average method, find the appropriate price like so:

3000/6000 = .5 <--- The already started units cost $0.50 per unit.
25,560/50000 = .5112 <--- The units started from scratch cost $0.5112 per unit.

Now average: (.5 + .5112)/2 = $0.51 <--- this is the weighted average per unit.

Now take the weighted average and multiply by the units in WIP at Oct 31.

$0.51 x 12,000 = $6,120

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