Show me the steps to solve Carpenter Corporation uses the weighted$-$average method in its process costing system. This month, the beginning inventory in the first processing department consisted of $600$ units. The costs and percentage completion of these units in beginning inventory were:

Cost Percent Complete

Materials costs $ $5,20060\%$

Conversion costs $ $8,50055\%$

A total of $7,800$ units were started and $7,100$ units were transferred to the second processing department during the month. The following costs were incurred in the first processing department during the month:

Cost

Materials costs $ $95,000$

Conversion costs $ $169,200$

The ending inventory was $85\%$ complete with respect to materials and $70\%$ complete with respect to conversion costs.

The total cost transferred from the first processing department to the next processing department during the month is closest to:

Note: Round "Cost per equivalent unit" to $3$ decimal places.