Factory overhead costs for a given period were 1.5 times as much as the direct material costs. Prime costs totaled $15,500. Conversion costs totaled $22,725. What are the direct labor costs for the period?

The direct labor costs for the period is $1,050

Explanation:

Here in this question, we are concerned with calculating the direct labor costs for the period.

To calculate this, we employ a mathematical approach.

Let the direct material cost for the period be $y.

Mathematically, direct labor cost = Prime costs - direct material cost

From the question, Prime costs = $15,500

Thus, the direct labor cost = $15,500 -$y

Mathematically also;

Conversion costs = Direct labor costs + Factory overheads

But from the question, we know that the factory overheads = 1.5 * direct material costs = 1.5 * y = 1.5y

Thus by adding the factory overheads to the direct labor cost and equating to the conversion factor, we have;

1.5y + 15500-y = 22,725

1.5y -y = 22,725 - 15500

0.5y = 7225

y = 7225/0.5

y = $14,450

Recall;

Direct labor costs = Prime costs - direct material costs

Direct labor cost = 15,500 - 14,450 = $1,050