Tambin Inc. produces a gasoline additive that, when added to the gas tank of the average automobile, is designed to increase gas mileage by $15\%.$ 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;

conversion $50\%$ complete$)33,000$ $ $68,000$

Finished goods, December $3138,000$ $ $121,500$

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$)28,000$ $ $30,000$ $ $56,000$

Started into production $765,000$

Costs added during the year $ $758,000$ $ $2,080,000$

Units completed during the year $760,000$

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.$)$