At the beginning of the month, the Painting Department of Skye Manufacturing had 20,000 units in inventory, $$ 70 \% $$ complete as to materials, and $$ 20 \% $$ complete as to conversion. The cost of the beginning inventory, $$ \$ 28,650 $$, consisted of $$ \$ 22,400 $$ of material costs and $$ \$ 6,250 $$ of comversion costs. During the month the department started 115,000 units and transferred 120,000 units to the next manufacturing department. Costs added is the current month consisted of $$ \$ 229,600 $$ of materials costs and $$ \$ 540,500 $$ of conversion costs. At the end of the month, the department had 15,000 units in inventory, $$ 40 \% $$ complete as to materials and $$ 10 \% $$ complete as to conversion. If Skye Manufacturing uses the weighted average method of process costing, compute the costs per equivalent unit of materials and conversion respectively for the Painting Department.

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**Step 1. Compute Equivalent Units of Production**

Under the weighted average method, the total equivalent units are computed by summing the completed (transferred) units plus the work-in-process (WIP) units at the end of the period.

1. **Materials:**  
   - Units transferred out: $$120{,}000$$ units (each 100% complete for materials)  
   - Ending inventory: $$15{,}000$$ units $$\times 40\%$$ complete $$= 15{,}000 \times 0.40 = 6{,}000$$ equivalent units  
     
   Therefore, total equivalent units for materials:  
   $$
   120{,}000 + 6{,}000 = 126{,}000 \text{ units}
   $$

2. **Conversion:**  
   - Units transferred out: $$120{,}000$$ units (each 100% complete for conversion)  
   - Ending inventory: $$15{,}000$$ units $$\times 10\%$$ complete $$= 15{,}000 \times 0.10 = 1{,}500$$ equivalent units  
     
   Therefore, total equivalent units for conversion:  
   $$
   120{,}000 + 1{,}500 = 121{,}500 \text{ units}
   $$

---

**Step 2. Determine Total Costs to be Allocated**

Total costs include costs in the beginning inventory plus the costs added during the current month.

1. **Materials:**
   - Beginning inventory: $$\$22{,}400$$
   - Costs added during the month: $$\$229{,}600$$
     
   Total materials cost:
   $$
   22{,}400 + 229{,}600 = \$252{,}000
   $$

2. **Conversion:**
   - Beginning inventory: $$\$6{,}250$$
   - Costs added during the month: $$\$540{,}500$$
     
   Total conversion cost:
   $$
   6{,}250 + 540{,}500 = \$546{,}750
   $$

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**Step 3. Calculate the Cost per Equivalent Unit**

1. **Materials:**  
   $$
   \text{Cost per equivalent unit for materials} = \frac{\$252{,}000}{126{,}000} = \$2.00
   $$

2. **Conversion:**  
   $$
   \text{Cost per equivalent unit for conversion} = \frac{\$546{,}750}{121{,}500} = \$4.50
   $$

---

**Final Answer:**

- Cost per equivalent unit for materials: $$\$2.00$$  
- Cost per equivalent unit for conversion: $$\$4.50$$
- Cost per equivalent unit for materials: \$2.00 - Cost per equivalent unit for conversion: \$4.50

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