Each of the 20 employees at Company J is to receive an end-of-year bon

Agnes = Cheryl + 500
The remaining 18 employees >= Cheryl
Total = 60000
—> in order Agnes to get the largest bonus, the any other employees should get the same as Cheryl gets.

19Ch + Ch + 500 = 60000
20 Ch = 59500
Ch = 2975
—> Agnes = 2975 + 500 = 3475

Answer ( D)

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We can let the bonus of Cheryl and the other employees = 19x and Agnes’s bonus = x + 500; thus:

20x + 500 = 60,000

20x = 59,500

x = 2,975

Thus, Agnes will receive 2,975 + 500 = $3,475 in bonus.

Answer: D


_________________

given
total employees = 20
A received 500+ C
and all 18 other receive same salary as C ;
so we have
19c+500+c = 60,000
solve for c= 2975
a salary ; 2975+500 ; 3475
OPTION D

Each of the 20 employees at Company J is to receive an end-of-year bonus this year. Agnes will receive a larger bonus than any other employee, but only $500 more than Cheryl will receive. None of the employees will receive a smaller bonus than Cheryl. If the amount of money to be distributed in bonuses at Company J this year totals $60,000, what is the largest bonus Agnes can receive?

A. $3,250
B. $3,325
C. $3,400
D. $3,475
E. $3,500

Now, if everybody had got the same amount in bonus, then each would have got $60,000/20 = $3000
but since Agnes must receive only $500 more than Cheryl and none of the employees must take less than Cheryl, Agnes' bonus gets max if all other than Agnes receive bonus equal to Cheryl. Since there are 20 employees, all including Agnes must take a cut of $500/20 = $25. So, Agnes takes $3000 + $500 - $25 = $3475. Hence, D is the answer

Hi,
As Agnes' bonus is 500$ more than Cheryl, let's call it A=C+500
For Agnes to have the max bonus, all the other must have the same minimum, therefore all the 18 other employees and Cheryl must have the same bonus amount: we get 19C

60000=19C+C+500
59500=20C
C=2975$

Now as Agnes = C+500, Agnes will get 2975+500= 3475$ max

Answer D)

 

This means that Cheryl has the smallest bonus and others could have it too. But Agnes has the highest bonus (more than all others) and it is $500 more than Cheryl's bonus. Say Cheryl's bonus is $c.

If we arrange all bonuses in increasing order, we could get something like:
$c, $c, $(c + 10), $(c + 200), ... $(c + 500)

If we want to maximise Agnes' bonus we should minimize that of all others so that Agnes can get the biggest part of $60,000.

So 19 people can get $c while Agnes gets $(c + 500). 

19c + c + 500 = 60,000
c = 2975

c + 500 = $3475

Answer (D)

Check out this blog post for another question on mean, median and range.



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Agnes's bonus will be maximized when all other employees receive the same bonus as Cheryl. The equation is : 19x + x +500 =60,000 or, 20x = 59,500 so, x = 2975. Agnes's bonus = 2975 +500 = 3475

1. In order to maximize the bonus to Agnes, we need to minimize the bonus' paid to each of the other employees

2. Let the bonus paid to Agnes be \(A\)

3. \(A + [(A - 500) * 19] = 60000\)

4. \(A + 19A - 9500 = 60000\) -> \(20A = 69500\) -> \(A = 3475\)

Ans. D

Hi, I wanted to check on the line "None of the employees will receive a smaller bonus than Cheryl". Why did we not take this into account in solving the answer?

­Hi JoeSal,

It is taken into account, but it basically means that the employees will recieve a bonus in this order

Agnes > 19 other employees >or= Cheryl


Basically, whatever bonus amount Cheryl recieves is the lowest limit for what the other 19 employees may recieve.

So, the employees can recieve at the very least the amount that Cheryl has recieved.

Since this is the case, it can also be that the amount recieved by Cheryl is the amount recieved by the 18 other employees apart from Agnes (since Agnes = Cheryl + 500)­