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# Total boarding expenses of a boarding house are partly fixed and partl

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Math Expert
Joined: 02 Sep 2009
Posts: 61385
Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

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16 Jan 2020, 03:09
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Difficulty:

75% (hard)

Question Stats:

39% (02:20) correct 61% (02:47) wrong based on 18 sessions

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Total boarding expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is $700 when there are 25 boarders and$600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?

A. $500 B.$510
C. $520 D.$530
E. $550 _________________ Intern Joined: 24 May 2013 Posts: 7 Re: Total boarding expenses of a boarding house are partly fixed and partl [#permalink] ### Show Tags 20 Jan 2020, 06:06 2 Let the fixed cost be x and the variable cost be y per boarder. Then, x + 25y = 700 × 25 ⇒ x + 25y = 17500.....(i) x + 50y = 600 × 50 ⇒ x + 50y = 30000.....(ii) Subtracting (i) from (ii), we get: 25y = 12500 ⇒ y = 500 Putting y = 500 in (i), we get: x = 5000 Therefore, total expenses of 100 boarders = x + 100y = 5000 + (500 × 100) = 55000 Hence, average expense = 55000/100 = 550 Answer: E Manager Joined: 22 Sep 2018 Posts: 67 Re: Total boarding expenses of a boarding house are partly fixed and partl [#permalink] ### Show Tags 21 Jan 2020, 00:43 1 in this question it is given the average expenses for each group. so let a be fixed price for x people and b be the price for extra people for 25 members $$\frac{x*a + (25-x)*b }{ 25} = 700$$ for 50 members $$\frac{x*a + ( 50-x)*b }{ 50} = 600$$ solving above we get b = 500 for 100 members $$\frac{x*a + ( 100-x)*b }{ 100} = \frac{x*a + ( 50-x)*b + 50*b }{ 100} = \frac{5500}{100} = 550$$ e-GMAT Representative Joined: 04 Jan 2015 Posts: 3250 Re: Total boarding expenses of a boarding house are partly fixed and partl [#permalink] ### Show Tags 21 Jan 2020, 08:05 1 Solution Given In this question, we are given that • Total boarding expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. • The average expense per boarder is$700 when there are 25 boarders and $600 when there are 50 boarders. To find We need to determine • The average expense per boarder when there are 100 boarders Approach and Working out Let us assume that the fixed expense is F and the variable expense per boarder is V. When there are 25 boarders, the average expense per boarder is$700
• F + 25V = 25 x 700 = 17500

When there are 50 boarders, the average expense per boarder is $600 • F + 50V = 50 x 600 = 30000 Solving the two equations above, we get F = 5000 and V = 500 Hence, the total expense when there are 100 boarders = 5000 + 100 x 500 = 55000 • Average expense per boarder = 55000/100 =$550

Thus, option E is the correct answer.

_________________
Re: Total boarding expenses of a boarding house are partly fixed and partl   [#permalink] 21 Jan 2020, 08:05
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