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# In Dives Corporation, 75% of the employees are customer service repres

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Math Expert
Joined: 02 Sep 2009
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In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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04 Dec 2017, 03:08
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In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of$100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers? A.$140,000
B. $180,000 C.$260,000
D. $400,000 E.$560,000
[Reveal] Spoiler: OA

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Re: In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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04 Dec 2017, 03:20
imo D
let total # of employees be 100 & the average salary of the managers be x
sum of salaries = average salary* number of employees
$$10^7$$= (60,000*75) +($$10^5$$ *15) + 10x
$$10^7$$= 45*$$10^5$$ + 15*$$10^5$$ +10x
$$10^5$$(100-60)=10x
x= 400,000
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Re: In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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04 Dec 2017, 03:21
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Bunuel wrote:
In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of$100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers? A.$140,000
B. $180,000 C.$260,000
D. $400,000 E.$560,000

40....100....x (Distance from Mean)

75 * 40 = x * 10
x = 30
Salary of manager = 30 + 10 = 40
D
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In Dives Corporation, 75% of the employees are customer service repres [#permalink]

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11 Dec 2017, 09:30
Bunuel wrote:
In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of $60,000, and the programmers have an average salary of$100,000. If the average salary of all employees is also $100,000, what is the average salary of the managers? A.$140,000
B. $180,000 C.$260,000
D. $400,000 E.$560,000

Weighted average approach.* For easier calculation, remove three zeros from salaries (divide all by 1,000). Obviously, put them back for the answer.

Percentages sum to 100, in decimal form, = 1. They are the weight.
Salaries are the average for each group.
Let $x = managers' average salary Customer service: .75($60)
Programmers: .15($100) Managers: .10($x)
Total weight: (.75 + .15 + .10 = 1)
Overall average salary: $100 .75($60) + .15($100) + .10($x) = (1)($100)$45 + $15 + .10x =$100
.10x = $40 $$x = \frac{40}{.10}=400$$ (put three zeros back, i.e.,$400 * 1,000)
x = $400,000 Answer D *$$(W_1)(A_1) + (W_2)(A_2) + (W_3)(A_3) = (W{1+2+3})(A_{overall})$$ _________________ At the still point, there the dance is. -- T.S. Eliot Formerly genxer123 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 2069 Location: United States (CA) Re: In Dives Corporation, 75% of the employees are customer service repres [#permalink] ### Show Tags 12 Jan 2018, 06:29 Bunuel wrote: In Dives Corporation, 75% of the employees are customer service representatives, 15% are programmers, and 10% are managers. The customer service representatives have an average salary of$60,000, and the programmers have an average salary of $100,000. If the average salary of all employees is also$100,000, what is the average salary of the managers?

A. $140,000 B.$180,000
C. $260,000 D.$400,000
E. \$560,000

We can let n = the average salary of the managers and create the equation:

0.75(60,000) + 0.15(100,000) + 0.1n = 100,000

45,000 + 15,000 + 0.1n = 100,000

0.1n = 40,000

n = 400,000

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Re: In Dives Corporation, 75% of the employees are customer service repres   [#permalink] 12 Jan 2018, 06:29
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