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

It is currently 02 Apr 2020, 23:29

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: 62457
Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

Show Tags

New post 16 Jan 2020, 03:09
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

37% (02:20) correct 63% (02:47) wrong based on 19 sessions

HideShow timer Statistics

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
Intern
avatar
B
Joined: 24 May 2013
Posts: 8
Re: Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

Show Tags

New post 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
Manager
avatar
S
Joined: 22 Sep 2018
Posts: 76
Re: Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 04 Jan 2015
Posts: 3338
Re: Total boarding expenses of a boarding house are partly fixed and partl  [#permalink]

Show Tags

New post 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.

Correct Answer: Option E
_________________
GMAT Club Bot
Re: Total boarding expenses of a boarding house are partly fixed and partl   [#permalink] 21 Jan 2020, 08:05
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