Beginning inventory and purchases as follows:

Beg Inv... 7 @ $104
1st purch... 12 @ $103
2nd purch... 19 @ $105
3rd purch... 11 @ $107

Use periodic system. 19 units were left in inventory at the end of the period.
Determine the cost of the 19 units in the inventory by each method, show work.

1) FIFO
2) LIFO
3) average cost

You have 49 total units available. 19 are left in ending inventory and therefore 30 were sold.

When using FIFO, that means you're using the costs of the ones purchased first. i.e. you sell the 7 @ $104 first, then the 12 @ $103, etc. So if you're selling them in order from the top, which ones must be left over in ending inventory?

The same works for LIFO, except it's the opposite. You're selling starting with the last purchase, so you first sell the 11 @ $107, then the 19, etc. So if you're selling in order from the top, again, which ones must be left over in ending inventory.

For average, you need to average all 49 of them. i.e. it's not just take four prices, adding them and dividing by 4. Because you don't have one of each price. You only have 7 at $104, but you have 19 at $105... so the 19 counts more into the average. This would like if you listed $104 seven times, then $103 twelve times, added them all and divided by the 49 total. But the fast way is:
7 x $104 = $428
12 x $103 =?

Etc. This way you account for all 49 of them. You take the total prices and divide by 49 items to get an average. Once you have the average, you can figure out the cost of the 19 in ending inventory.