Math Problem Statement

A company purchased inventory as follows: 150 units at $6 and 350 units at $7. The average unit cost for inventory is:

Solution

To find the average unit cost for inventory, we use the weighted average formula:

Average Unit Cost=Total Cost of InventoryTotal Units\text{Average Unit Cost} = \frac{\text{Total Cost of Inventory}}{\text{Total Units}}

Step 1: Calculate Total Cost

  1. For 150 units at $6: 150×6=900150 \times 6 = 900
  2. For 350 units at $7: 350×7=2450350 \times 7 = 2450

The total cost of inventory is: 900+2450=3350900 + 2450 = 3350

Step 2: Calculate Total Units

The total number of units is: 150+350=500150 + 350 = 500

Step 3: Find the Average Unit Cost

Substitute into the formula: Average Unit Cost=Total CostTotal Units=3350500=6.70\text{Average Unit Cost} = \frac{\text{Total Cost}}{\text{Total Units}} = \frac{3350}{500} = 6.70

Final Answer:

The average unit cost for inventory is $6.70.

Correct Option: c. $6.70


Would you like me to provide more detailed steps or any clarifications? Let me know!

Here are 5 related questions to expand your understanding:

  1. How would the average unit cost change if more units at $8 were added?
  2. What is the difference between weighted average cost and FIFO methods in inventory valuation?
  3. If only 50 units were sold, how would you calculate the ending inventory value?
  4. How does the average cost method impact financial statements during inflation?
  5. If prices are decreasing, which inventory method (FIFO, LIFO, or average cost) is most favorable?

Tip: In inventory costing, the weighted average cost method smooths out price fluctuations over time.

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Math Problem Analysis

Mathematical Concepts

Weighted Average
Inventory Costing

Formulas

Average Unit Cost = Total Cost of Inventory / Total Units

Theorems

Weighted Average Formula

Suitable Grade Level

Grades 9-11