I have a homework problem and I keep trying to do it and I don't think I am doing it correctly . Here's is the question:

Beginning Inventory: 6 units at $83 $498

First Purchase: 10 units at $82 $820

Second Purchase: 18 units at $84 $1512

Third Purchase: 10 units at $85 $850

44total units total $3680

The company uses the periodic system, and there were 15 units left in the inventory at the end of the period. Determine the cost of 12 of the units of inventory by each of the following methods, presenting details of your computations; a)first-in first-out method b)last-in first-out method and c) average cost method.

Here are my solutions:

First-in first-out method

Earliest costs 6 units at $83 $498

Next earliest costs 10 units at $82 $820

Next earliest costs 13 units at $84 $1092

29 total units $2410

$3680 - $2410 = $1270

(1270/15)12 = 1016

The total cost of 12 units of inventory is $1016.

Last-in First-out method

Most recent costs 10 units at $85 $850

Next most recent costs 18 units at $84 $1512

Next most recent costs 1 unit at $82 $82

29 total units $2444

$3680 - $2444 = $1236

(1236/15)12 = 988.80

The total cost of 12 units of inventory is $988.80.

Average Cost method

Average Unit Cost: $3680/44units=$83.636363636363636363636363636364

Cost of Merchandise Sold = 29 units at $83.636363636363636363636363636364 = 2425.45

$3680 - $2425.45 = $1254.55

(12.54.55/15)12 = 1003.64

The total cost for 12 units of inventory is $1003.64.

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Basically I am pretty sure that I am not doing this correct but I can't seem to figure out where I am going wrong and why. If someone could please explain where I am going wrong I would really appreciate it. Thanks.