Tambin Inc. produces a gasoline additive that, when added to the gas tank of the average automobile, is designed to increase gas mileage by $20\%.$ The company$$s controller suspects that the year$-$end dollar balances shown below in the inventory accounts may be incorrect.

Units Costs

Work in process, December $31($materials $100\%$ complete; $41,000$ $ $76,000$

conversion $50\%$ complete$)$

Finished goods, December $3146,000$ $ $129,500$

There were no finished goods inventories at the beginning of the year. The company uses the weighted$-$average method of process costing. There is only one processing department.

A review of the company$$s inventory and cost records shows the following:

Costs

Units Materials Conversion

Work in process, beginning of year $($materials $100\%$ complete; conversion $80\%$ complete$)36,000$ $ $38,000$ $ $64,000$

Started into production $845,000$

Costs added during the year $ $766,000$ $ $2,160,000$

Units completed during the year $840,000$

Required:

$1.$Determine the equivalent units and the costs per equivalent unit for materials and conversion for the year.$($Round your "Cost per equivalent unit" answers to $2$ decimal places.$)$

$2.$Determine the amount of cost that should be assigned to the ending work in process and finished goods inventories.

$3.$Prepare the necessary correcting journal entry to adjust the work in process and finished goods inventories to the correct balances as of December $31.($Round intermediate calculations to $2$ decimal places.$)$