Question

Joint-Serve Prosthetics spends 43% of its total expenses for payroll. It increased its total expenses when it spent $250,000 for robotic assemblers. This changed the allocation for payroll to 38% of total expenses. What were its total expenses after purchasing the robotic assemblers? Hint: First find the total expense before the purchase of robotic assemblers.

Answer 1

Answer: $2,150,000

Explanation: Let

T = Total expenses of Joint-Serve

Then, before the company acquired robotic assemblers, the expenses allocated for payroll is given by

Expenses for Payroll = 43% of Total Expenses
Expenses for Payroll = 0.43T (1)
(Because 43% = 0.43)

Because the total expenses increased by $250,000 after spending for robotic assemblers, the total expenses = T + 250,000

So, the payroll expense is now calculated as

Expenses for Payroll = 38% of Total Expenses
Expenses for Payroll = 0.38(T + 250,000) (2)
(Because 38% = 0.38 and total expenses = T + 250,000)

By comparing equations (1) and (2),


`0.43T = 0.38(T + 250,000) \\ 0.43T = 0.38T + 0.38(250,000) \\ 0.43T = 0.38T + 95,000 \\ 0.43T - 0.38T = 95,000 \\ (0.05T)/(0.05) = (95,000)/(0.05) \\ \boxed{T = \$ 1,900,000}`

Thus, the total expense before the purchase of robotic assemblers is T = $ 1,900,000. Therefore, the total expense after purchasing the robotic assemblers is T + 250,000 = 1,900,000 + 250,000 = $2,150,000