Answer: Let's assume that the direct material costs for the period are x. Then, from the information given in the problem:
Factory overhead costs for the period were 2 times as much as the direct material costs, so the factory overhead costs are 2x.
Prime costs, which is the sum of direct material costs and direct labor costs, totaled $10,100. Therefore, we can write the equation:
x + Direct labor costs = 10,100
Conversion costs, which is the sum of direct labor costs and factory overhead costs, totaled $14,150. Therefore, we can write the equation:
Direct labor costs + 2x = 14,150
Now, we can solve for the direct labor costs by using the two equations we have. First, we can substitute x + Direct labor costs = 10,100 into the second equation:
Direct labor costs + 2x = 14,150
Direct labor costs = 14,150 - 2x
x + Direct labor costs = 10,100
x + (14,150 - 2x) = 10,100
14,150 - x = 10,100
x = 4,050
So, the direct material costs for the period are $4,050. Now, we can substitute this value into the equation for direct labor costs:
Direct labor costs + 2x = 14,150
Direct labor costs + 2(4,050) = 14,150
Direct labor costs = 14,150 - 2(4,050)
Direct labor costs = $6,050
Therefore, the direct labor costs for the period are $6,050.