Using the reciprocal services method, which of the following equations represents the correct algebraic expression to determine Janitorial Department costs when the total costs of the Janitorial Department (J) include not only $500,000 of direct costs but also 25% of the Maintenance Department (M) cost and the Maintenance Department includes not only $450,000 of direct costs but also 30% of the Janitorial Department? (Hint: This equation is derived from the two separate equations representing each department's costs.)
A)J = $500,000 + [(0.25 ÷ $450,000) + (0.30 ÷ J)]
B)J = ($500,000 × 0.25) + [($450,000 × 0.20) + J]
C)J = $500,000 - (0.25 × $450,000) - (0.20 × J)
D)J = $500,000 + {0.25 × [$450,000 + (0.20 × J)]}

Question

Quizplus · Accepted Answer

The correct equation takes into account the direct costs of the Janitorial Department ($500,000) and adds 25% of the total Maintenance Department costs. The Maintenance Department's total costs include its direct costs ($450,000) plus 30% of the Janitorial Department's costs (represented as 0.30 × J). This interdependency is correctly captured in option D, where the Janitorial Department's costs include its direct costs plus 25% of the Maintenance Department's total costs, which in turn include its direct costs and 30% of the Janitorial Department's costs.

Using the Reciprocal Services Method, Which of the Following Equations