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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: 62637
Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

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16 Jan 2020, 03:11
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Difficulty:

15% (low)

Question Stats:

83% (02:02) correct 17% (02:08) wrong based on 47 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 total boarding expenses is \$1200 when there are 40 boarders and is \$1500 when there are 55 boarders. What is the total boarding expenses when there are 75 boarders?

A. \$1800
B. \$1900
C. \$2000
D. \$2100
E. \$2200

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

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21 Jan 2020, 00:03
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1
let x be the standard count, where the price is fixed, and a is the first fixed price and b is the price for the xtra members

consider the 40 members,
a*x + (40-x)*b=1200
consider the 55 members
a*x + (55-x)*b=1500

solving both the equations we get b = 20\$

now consider the 75 members , as we don't the values of x and a , we can still get the answer in this case by modifying the equation into either one of the equations above

a*x + (75-x)*b
a*x + (55+20-x)*b
a*x + (55-x)*b + 20*b

1500+20*20 = 1900 \$

option B is correct.
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Joined: 04 Jan 2015
Posts: 3348
Re: Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

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21 Jan 2020, 08:16
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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 total boarding expenses is \$1200 when there are 40 boarders and is \$1500 when there are 55 boarders.

To find
We need to determine
• The total boarding expenses when there are 75 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 40 boarders, the total expense is \$1200
• F + 40V = 1200

When there are 55 boarders, the total expense is \$1500
• F + 55V = 1500

Solving the two equations above, we get F = 400 and V = 20

Hence, the total expense when there are 75 boarders = 400 + 75 x 20 = 1900

Thus, option B is the correct answer.

Correct Answer: Option B
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Re: Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

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23 Jan 2020, 09:03
1
Bunuel wrote:
Total boarding expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The total boarding expenses is \$1200 when there are 40 boarders and is \$1500 when there are 55 boarders. What is the total boarding expenses when there are 75 boarders?

A. \$1800
B. \$1900
C. \$2000
D. \$2100
E. \$2200

Solution:

We can set up the equation y = k + nx, where y is the total expenses when there are x boarders and k and n are some constants. Thus, we can create the equations:

1200 = k + 40n

1200 - 40n = k

and

1500 = k + 55n

Substituting, we have:

1500 = 1200 - 40n + 55n

300 = 15n

20 = n

Thus, k = 1200 - 40(20) 1200 - 800 = 400.

So, when there are 75 boarders, the cost is:

400 + 75(20) = 400 + 1500 = 1900

Alternate Solution:

Since the boarding expenses vary linearly with the number of boarders, we see that 55 - 40 = 15 boarders cost 1500 - 1200 = 300 dollars more in boarding expenses. That is, an extra boarder would cost 300/15 = 20 dollars more in boarding expenses. Since 75 - 55 = 20, 75 boarders would cost 20 x 20 = 400 dollars more in boarding expenses than 55 boarders. Therefore, the total expenses of 75 boarders is 1500 + 400 = 1900 dollars.

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Re: Total boarding expenses of a boarding house are partly fixed and partl   [#permalink] 23 Jan 2020, 09:03
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# Total boarding expenses of a boarding house are partly fixed and partl

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