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Total expenses of a boarding house are partly fixed and partly varying

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Total expenses of a boarding house are partly fixed and partly varying  [#permalink]

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New post 02 Apr 2020, 06:32
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Total expenses of a boarding house are partly fixed and partly varying linearly with tile 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. 540
B. 550
C. 560
D. 560
E. 570

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Re: Total expenses of a boarding house are partly fixed and partly varying  [#permalink]

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New post 02 Apr 2020, 07:35
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let fixed expense be k and variying be x


then we have (k+25x)/25=700

(k+50x)/50=600

simplifying

k/25 + x =700

k/50 + x =600


we need to find k/100+x =?

easily solve and get 550

option c
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Re: Total expenses of a boarding house are partly fixed and partly varying  [#permalink]

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New post 02 Apr 2020, 07:47
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Bunuel wrote:
Total expenses of a boarding house are partly fixed and partly varying linearly with tile 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. 540
B. 550
C. 560
D. 560
E. 570


Total expenses = Fixed + Variable*number of boarders[/m]
\(TE(25) = F + V*25\); \(700*25 = F + V*25\) --a
\(TE(50) = F + V*50\); \(600*50 = F + V*50\) --b
subtracting the above equations a and b,
\(V*25=12500\); \(V=500\), put this value in one of the equations and we get F = 5000
thus, \(TE(100) = 5000 + 500*100\)
Avg Expense(100) = 50 + 500 = 550.
Ans: B
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Re: Total expenses of a boarding house are partly fixed and partly varying  [#permalink]

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New post 10 May 2020, 12:26
ArunSharma12 wrote:
Bunuel wrote:
Total expenses of a boarding house are partly fixed and partly varying linearly with tile 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. 540
B. 550
C. 560
D. 560
E. 570


Total expenses = Fixed + Variable*number of boarders[/m]
\(TE(25) = F + V*25\); \(700*25 = F + V*25\) --a
\(TE(50) = F + V*50\); \(600*50 = F + V*50\) --b
subtracting the above equations a and b,
\(V*25=12500\); \(V=500\), put this value in one of the equations and we get F = 5000
thus, \(TE(100) = 5000 + 500*100\)
Avg Expense(100) = 50 + 500 = 550.
Ans: B




Hey! I know my logic is incorrect because I got the question wrong, but not sure why. I read that it was linear in the question so automatically through y=mx+b… then I used the two points (25,700) and (50,600) to get a slope and y-intercept and then plugged 100 for x. It didn't work, but I'm confused on why it's not the correct method. Any color on this would be great, thanks!
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Re: Total expenses of a boarding house are partly fixed and partly varying  [#permalink]

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New post 11 May 2020, 05:42
Bunuel wrote:
Total expenses of a boarding house are partly fixed and partly varying linearly with tile 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. 540
B. 550
C. 560
D. 560
E. 570


∑_25 = 17500
∑_50 = 30000

Thus, Fixed cost is 5000 , SO variable cost per boarder is $ 500

So, Total Cost of 100 boarder is \(\frac{5000 + 5*100}{100} = 550\), Thus Answer must be (B)
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Re: Total expenses of a boarding house are partly fixed and partly varying  [#permalink]

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New post 11 May 2020, 10:00
25 boarders x 700 = 17500
50 boarders x 600 = 30000
Increment of 25 costs 12500
100 boarders = 12500x2 + 30000 =55000
answer is 550
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Re: Total expenses of a boarding house are partly fixed and partly varying  [#permalink]

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New post 12 May 2020, 16:44
tarasovk wrote:
25 boarders x 700 = 17500
50 boarders x 600 = 30000
Increment of 25 costs 12500
100 boarders = 12500x2 + 30000 =55000
answer is 550


Thank you for the smart approaches!!!!

I would like to know what is wrong with my approach. Since the decrease per 25 boarders is 100 ($700 for 25 boarders and $600 for 50 boarders) then for me would be logical to assume that the average cost for 75 passengers would be $500 and for 100 passengers $400, in other words, $100 "discount" per 25 passengers.

Could you please help me?!

Thank you for the great answers
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Re: Total expenses of a boarding house are partly fixed and partly varying  [#permalink]

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New post 15 May 2020, 05:25
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Bunuel wrote:
Total expenses of a boarding house are partly fixed and partly varying linearly with tile 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. 540
B. 550
C. 560
D. 560
E. 570


Since the total expenses is linear, we let it be y = mx + b where y is the total expense, m is the expense per boarder, x is the number of boarders, and b is the fixed cost. Using the information from the problem, we see that the total expenses are 25 x 700 = $17,500 when there are 25 boarders and 50 x 600 = $30,000 when there are 50 boarders. So we can create the equations:

25m + b = 17,500

and

50m + b = 30,000

Subtracting the first equation from the second, we have:

25m = 12,500

m = 500

Since m = 500, we have:

50(500) + b = 30,000

25,000 + b = 30,000

b = 5,000

Therefore, the total expenses equation is y = 500x + 5,000, and for 100 boarders, the total expenses are:

y = 500(100) + 5,000 = 50,000 + 5,000 = 55,000

Therefore, the average expense per boarder is 55,000/100 = $550 when there are 100 boarders.

Answer: B
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Re: Total expenses of a boarding house are partly fixed and partly varying   [#permalink] 15 May 2020, 05:25

Total expenses of a boarding house are partly fixed and partly varying

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