GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 29 Feb 2020, 02:43

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61537
Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

Show Tags

New post 16 Jan 2020, 03:11
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (02:01) correct 19% (02:08) wrong based on 43 sessions

HideShow timer Statistics

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

_________________
Manager
Manager
avatar
S
Joined: 22 Sep 2018
Posts: 71
Re: Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

Show Tags

New post 21 Jan 2020, 00:03
2
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.
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3276
Re: Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

Show Tags

New post 21 Jan 2020, 08:16
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 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
_________________
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9542
Location: United States (CA)
Re: Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

Show Tags

New post 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.


Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: Total boarding expenses of a boarding house are partly fixed and partl   [#permalink] 23 Jan 2020, 09:03
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne