Question

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 × 0.20) + J]

b.J = $500,000 – (0.25 × $450,000) – (0.20 × J)

c.J = $500,000 + [(0.25 ÷ $450,000) + (0.30 ÷ J)]

d.J = $500,000 + {0.25 × [$450,000 + (0.20 × J)]}

Answer 1

Let the total cost of Janitorial Dept and Maintenance Dept be J and M
Therefore, J =		$ 500000 + 0.25M
	M =	$ 450000 + 0.30J
	Putting the value of M in equ. (i), we get
	J =	$ 500000 + [0.25 x ($ 450000 + 0.30 x J)]

Answer: Option d