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As a salesperson, Alice can choose one of two methods of annual paymen

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As a salesperson, Alice can choose one of two methods of annual paymen  [#permalink]

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New post 21 Dec 2017, 04:11
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As a salesperson, Alice can choose one of two methods of annual payment: either an annual salary of $45,500 with no commission or an annual salary of $12,500 plus a 25 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

A. $115,000
B. $132,000
C. $165,000
D. $182,000
E. $195,000

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Re: As a salesperson, Alice can choose one of two methods of annual paymen  [#permalink]

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New post 21 Dec 2017, 04:25
Bunuel wrote:
As a salesperson, Alice can choose one of two methods of annual payment: either an annual salary of $45,500 with no commission or an annual salary of $12,500 plus a 25 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

A. $115,000
B. $132,000
C. $165,000
D. $182,000
E. $195,000


Alice can choose one of two methods of annual payment: either an annual salary of $45,500=an annual salary of $12,500 plus a 25 percent commission on her total annual sales

So 45,500=12,500+(1/4)x

x=132,000

Hence B
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Re: As a salesperson, Alice can choose one of two methods of annual paymen  [#permalink]

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New post 21 Dec 2017, 10:59
Bunuel wrote:
As a salesperson, Alice can choose one of two methods of annual payment: either an annual salary of $45,500 with no commission or an annual salary of $12,500 plus a 25 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

A. $115,000
B. $132,000
C. $165,000
D. $182,000
E. $195,000


Since the correct answer is right there in front of us, let's use the answers! This is an Alternative approach.

Let's start with the median - C. If her annual sales are 165,000, Alice's commission is 25% * 165,000 = a bit more than 40,000.
Then her total salary is a bit more than 12,500 + 40,000 = 52,500 - too much!
(C) is eliminated as are the larger (D) and (E).
Let's try B. Then Alice's commission is 25% * 132,000 = 25% * (120,000 + 12,000) = 30,000 + 3,000 = 33,000
Her total salary in this case is 33,000 + 12,500 = 45,500. Yes!

(B) is our answer.
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As a salesperson, Alice can choose one of two methods of annual paymen  [#permalink]

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New post 21 Dec 2017, 11:21
Bunuel wrote:
As a salesperson, Alice can choose one of two methods of annual payment: either an annual salary of $45,500 with no commission or an annual salary of $12,500 plus a 25 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

A. $115,000
B. $132,000
C. $165,000
D. $182,000
E. $195,000



To figure out Alice's annual sales, we must determine the total commission that Alice earned to break even with the $45,500 salary

$45,500 - $12,500 = $33,000 --> Total commission that Alice must earn to break even with $45,500 salary.

Next, we can determine Alice's annual sales (X)

X = 33,000/.25 OR 33,000/x=1/4 --> 33,000(4)=x

$132,000 = x --> The answer is B
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As a salesperson, Alice can choose one of two methods of annual paymen   [#permalink] 21 Dec 2017, 11:21
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