There is nothing tricky about this. It is just a matter of applying the logic used in different inventory valuation methods. it is something you have to study and learn. You have some inventory to begin with, you buy some more, and you sell some leaving you some inventory at the end of the year. In a periodic system, sales are recorded at the time of sale, but cost of goods sold is calculated at the end of the accounting period. You get different cost of goods sold and ending inventory, depending on the inventory valuation method that is used.

Beginning inventory - 1,700 @ 45 = 76,500

Purchase . .3,800 @ 56 = 212,800

Purchase . . 2,500 @ 75 = 187,500

Goods available - - 8,000 units = 476,800

You sold 4,700 units so you must have 3,300 units left

LIFO. - You assume that what was sold are the latest units purchased.

2,500 units sold cost $75 each = 187,500

2,200 units sold cost $56 each = 123,200

4,700 units: cost of goods sold = 310,700

Total available - total sold = ending inventory

476,800 - 310.700 = 166,100

You can also verify the ending inventory:

Beginning = 1,700 units = 76,500

1,600 units left of the first purchase = 89,600

Total ending inventory - 3,300 units = 166,100

Now you can do the same with FIFO but you assume that the units sold are the ones you had in the beginning plus the earliest purchases. What is left in ending inventory are the latest purchases.

As for weighted average. You had a total cost of 476,800. divide by the total 8,000 units to find the average cost. then the units sold is multiplied by the average cost to get Cost of Goods Sold, and the units remaining multiplied by average cost is ending inventory.

Finally, specific identification: You know exactly what the cost is of the sold units.For the March sale, 40 units came from the beginning inventory and 60 came from the January purchase.

If I do all this for you, you would learn nothing. You learn it only by doing it. It is not tricky. It just needs care and logical thinking.