Cullumber Company uses a periodic inventory system and reports the following for the month of June. Date June 1 (a1) 12 23 30 Explanation Units Unit Cost Inventory Purchase Purchase Inventory 130 370 200 230 $5 Weighted-average unit cost $ 6 7 Total Cost $650 2,220 1,400 Calculate weighted-average unit cost. (Round answer to 3 decimal places, e.g. 5.125.)

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### Cullumber Company Inventory Report for June

Cullumber Company uses a periodic inventory system and reports the following for the month of June.

| Date       | Explanation | Units | Unit Cost | Total Cost |
|------------|-------------|-------|-----------|------------|
| June 1     | Inventory   | 130   | $5        | $650       |
| June 12    | Purchase    | 370   | $6        | $2,220     |
| June 23    | Purchase    | 200   | $7        | $1,400     |
| June 30    | Inventory   | 230   |           |            |

### Calculating Weighted-Average Unit Cost

To find the weighted-average unit cost, use the following formula:

\[ \text{Weighted-average unit cost} = \frac{\sum (\text{Units} \times \text{Unit Cost})}{\sum \text{Units}} \]

Using the given data:
1. Calculate the total cost for all units.
    - Initial Inventory: \(130 \times 5 = 650\)
    - First Purchase: \(370 \times 6 = 2220\)
    - Second Purchase: \(200 \times 7 = 1400\)

2. Add the totals: 
    - Total Units = \(130 + 370 + 200 = 700\)
    - Total Cost = \(650 + 2220 + 1400 = 4270\)

3. Apply the formula:
    - Weighted-average unit cost = \(\frac{4270}{700} = 6.1\)

\[ \boxed{6.1} \]

### Example Calculation:
\[ 
\frac{\sum (\text{Units} \times \text{Unit Cost})}{\sum \text{Units}} = \frac{650 + 2220 + 1400}{130 + 370 + 200} = \frac{4270}{700} = 6.1 
\]

Please round the final answer to three decimal places as per the given instruction, if necessary.
Transcribed Image Text:### Cullumber Company Inventory Report for June Cullumber Company uses a periodic inventory system and reports the following for the month of June. | Date | Explanation | Units | Unit Cost | Total Cost | |------------|-------------|-------|-----------|------------| | June 1 | Inventory | 130 | $5 | $650 | | June 12 | Purchase | 370 | $6 | $2,220 | | June 23 | Purchase | 200 | $7 | $1,400 | | June 30 | Inventory | 230 | | | ### Calculating Weighted-Average Unit Cost To find the weighted-average unit cost, use the following formula: \[ \text{Weighted-average unit cost} = \frac{\sum (\text{Units} \times \text{Unit Cost})}{\sum \text{Units}} \] Using the given data: 1. Calculate the total cost for all units. - Initial Inventory: \(130 \times 5 = 650\) - First Purchase: \(370 \times 6 = 2220\) - Second Purchase: \(200 \times 7 = 1400\) 2. Add the totals: - Total Units = \(130 + 370 + 200 = 700\) - Total Cost = \(650 + 2220 + 1400 = 4270\) 3. Apply the formula: - Weighted-average unit cost = \(\frac{4270}{700} = 6.1\) \[ \boxed{6.1} \] ### Example Calculation: \[ \frac{\sum (\text{Units} \times \text{Unit Cost})}{\sum \text{Units}} = \frac{650 + 2220 + 1400}{130 + 370 + 200} = \frac{4270}{700} = 6.1 \] Please round the final answer to three decimal places as per the given instruction, if necessary.
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