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

Question

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

A. $500
B. $510
C. $520
D. $530
E. $550

DUtkarsh · Accepted Answer

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

BhishmaNaidu99 · Answer

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

EgmatQuantExpert · Answer

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

CrackverbalGMAT · Answer

We see that as the number of boarders increase, the average price per boarder decreases.

When 25 doubles and becomes 50, the average price reduces by 100.

When 50 doubles and becomes 100, the reduction in price is 1/2 of the previous increase = 100/2 = 50

Therefore the average price will be 600 - 50 = $550

Option E

Arun Kumar

Abhishek009 · Answer

25*700 = F + 25v ------------------>(I)
 50*600 = F + 50v ------------------>(II)

Or,  30000 = 17500 -25v + 50v

Or,  12500 = 25v

Or,  v = 500  And  F = 17500 - 25*500 = 5000

Thus, average expense per boarder when there are 100 boarders is -

\frac{500*100 + 5000}{100}=550 , Answer must be (E)

Fdambro294 · Answer

(Total Expense) / (No. of Boarders) = Avg. price per boarder

Total Expense = (Fixed Cost - F) + ($Price per Boarder - P) * (Quantity of Boarders)

Avg. price per boarder = $700 ------> when there is 25 boarders

/ 25 = 700

F + 25p = 700(25) ---- (equation 2)

Avg. price per boarder = $600 ------> when there is 50 boarders

/ 50 = 600

F + 50p = 600(50) ----- (equation 1)

Combine the 2 Equations by Subtracting equation 2 from equation 1:

25p = 600(50) - 700(25)

---divide the entire equation on both sides by 25----

p = 600(2) - 700

p = $500 = price per Boarder

now, plug in p = $500 to determine the Fixed Cost = F

F + 50(p) = 600(50)

F + 50(500) = 600(50)

F = 600(50) - 50(500)

F = 6(5000) - 5(5000)

F = 1(5000) = $5,000 = Fixed Cost

Total Cost = $5,000 + $500 * (Q)

where Q = the quantity of boarders

Q: how much is Avg. Cost when there are 100 boarders?

(5,000 + 500(100)) / 100 =

(5,000 + 50,000) / 100 =

55,000 / 100 = $550

-E-

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards