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Each month, a certain manufacturing company's total expenses

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Each month, a certain manufacturing company's total expenses [#permalink] New post   18 Nov 2018, 03:14
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Each month, a certain manufacturing company's total expenses are equal to a fixed monthly expense plus a variable expense that is directly proportional to the number of units produced by the company during that month. If the company's total expenses for a month in which it produces 20,000 units are $570,000, and the total expenses for a month in which it produces 25,000 units are $705,000, what is the company's fixed monthly expense?

A. $27,000

B. $30,000

C. $67,500

D. $109,800

E. $135,000
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Re: Each month, a certain manufacturing company's total expenses [#permalink] New post   21 Dec 2021, 04:39
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Here we can call the Fixed Expense x and the Variable Expense y.

Therefore, we see that x + 20,000*y = 570,000, while x + 25,000*y = 705,000.

This simply gives us two equations and two unknowns so we can stack them up to eliminate the x-value:

x + 20,000*y = 570,000

x + 25,000*y = 705,000
----------------------

5000*y = 135,000

y = 135,000 / 5000 = 27

Now just plug this back into either equation to get the answer:

x + 27*20,000 = x + 540,000 = 570,000

==> x = 570,000 - 540,000 = 30,000.

Answer B.
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Re: Each month, a certain manufacturing company's total expenses [#permalink] New post   25 Nov 2018, 12:12
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Explanation:

Let F = fixed monthly expense

V = Variable expense.

As per 1st equation,

F + 20,000V = 570,000 ------------------(1)

and

F + 25,000V = 705,000 -------------------(2)

Solving equation (1) and (2)

V = 27.

Putting the value of V in equation 1,

F = 30,000, i.e Option B
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Re: Each month, a certain manufacturing company's total expenses [#permalink] New post   28 Oct 2020, 22:56
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We know TE=570k for 20k units and TE=705k for 25k units.

From this we can infer that there is a $135k difference for 5k units. So if 5000 units=$135000, then 1 unit=$27.

Now that we know this, we can say 570k=FE+(27*20k) so FE=30,000.
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Re: Each month, a certain manufacturing company's total expenses [#permalink]
28 Oct 2020, 22:56
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