C individuals pledged to pay equal contributions so that a charity...

Question

C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?

A) dx / C
B) x / (C-d)
C) d / (C-dx)
D) x / (C(C-d))
E) dx / (C(C-d))

Please develop in detail your answer.

Thank you.

A) dx / C
B) x / (C-d)
C) d / (C-dx)
D) x / (C(C-d))
E) dx / (C(C-d))

Please develop in detail your answer.

Thank you.

Kurtosis · Answer

Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = x
n = x/C

Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dx/C --> Additional amount

Number of individuals who are paying = C - d
Additional amount has to be divided among the (C - d) individuals --> dx/C(C - d)

Answer: E

hsbinfy · Answer

c people would pay x

1)so contra would be =x/c

2)but d people refused or didn't pay , so for same x contra increased to =x/(c-d)

note 2 nd point above has more contribution than 1 point above

so increase in contri is 2 statement - 1 statement above

x/c-d - x/c which will give you E as answer

DAllison2016 · Answer

\frac{x}{C} 	ext{ - original cost}\
\frac{x}{C-d} 	ext{ - new cost}\
	ext{additional cost = new cost - original cost}\
\frac{x}{C-d} - \frac{x}{C} = \frac{x(C)}{C(C-d)} - \frac{x(C-d)}{C(C-d)} = \frac{xd}{C(C-D)}

E) dx / (C(C-d))

JeffTargetTestPrep · Answer

Had all C individuals paid their contributions, each would have paid x/C dollars. Since d of them failed to pay theirs, each of the remaining individuals would now have to pay x/(C - d) dollars. Thus, the difference in the number of dollars contributed by each person is:

x/(C - d) - x/C

Obtaining the common denominator C(C - d), we have:

xC/  - x(C - d)/

/

(xC - xC + xd)/

xd/ 
 
Answer: E

aa008 · Answer

Algebraic solutions are already there, so Lets do it by assuming some values-

whenever you have to assume some values, make sure they in multiple.
It becomes easy to calculate later.

say x=$100, c=10, d=5

to reach $100, 10 people have to contribute $10 each.
5 of them did not give their share= 50$ was short
this $50 must be shared by remaining 5 people.

additional share the remaining people have to share= 50/5=  $10

we have x=$100, c=10, d=5, and our right answer should give you $10 after putting values of x,c and d.

E gives $10 as answer.

SO E is the correct answer.

RamSep · Answer

I've come up with a simple solution; Here is the logic that I used:
Total share of each person is  x/C . After failing  d  people to pay their shares, the total amount of their shares ( dx/C ) need to be paid by  C-d  individuals.
So, we get:  (dx/c)/(c-d)  and hence    dx/c(c-d) , choice E  .

TheGuyDangerous · Answer

Let t be the amount each person has to pay. => C*t = x => t= C/x

now, let n be the amount each person has to pay extra.

=> (C-d)*(t+n) = x

Solving and substituting t=X/C we get n as dX/C(C-d)

Ans E

pappal · Answer

if as pledged each of the C individuals paid its share, then per individual share= x/C
since d individuals failed to pay, so the total share that remain unpaid= (x/C)*d
now the additional burden on each of the left over (C-d) individuals=(dx/C)/(C-d)
=dx/C(C-d)
E

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