Pureform, Incorporated, uses the weighted$-$average method of process costing. It manufactures a product passing through two departments. Data for a recent month for the first department follow:

Units Materials Labor Overhead

Work in process inventory, beginning $5,000$ $ $4,320$ $ $1,040$ $ $1,790$

Units started in process $45,000$

Units transferred out $42,000$

Work in process inventory, ending $8,000$

Cost added during the month $ $52,800$ $ $21,500$ $ $32,250$

The beginning work in process inventory was $80\%$ complete for materials and $60\%$ complete for labor and overhead. The ending work in process inventory was $75\%$ complete for materials and $50\%$ complete for labor and overhead.

Required:

Compute the first department's equivalent units of production for materials, labor, and overhead for the month.

Determine the first department's cost per equivalent unit for materials, labor, and overhead for the month.