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Martha receives an annual salary of $20,000 plus a

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Martha receives an annual salary of $20,000 plus a

by BTGmoderatorDC » Fri Jul 27, 2018 6:40 pm

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Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000
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by Jay@ManhattanReview » Mon Jul 30, 2018 2:50 am
BTGmoderatorDC wrote:Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000
Say n = total annual sales

For Martha: Total Income = 20,000 + 10% of (n - 80,000)
For Sandra: Total Income = 30,000 + 5% of n

=> 20,000 + 10% of (n - 80,000) = 30,000 + 5% of n
20,000 + 0.1*(n - 80,000) = 30,000 + 0.05n
0.1n - 8,000 = 10,000 + 0.05n
0.05n = 18,000
n = 18,000/0.05 = 360,000

The correct answer: D

Hope this helps!

-Jay
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by swerve » Tue Jul 31, 2018 10:21 am
Let S be the sale when both the salaries are equal

So we have 20000 + 10% *(S-80000) = 30000 + 5%*S

Solving for S we get,

S = 360000

Hence, D is the correct answer. Regards!
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by Scott@TargetTestPrep » Wed Aug 01, 2018 3:33 pm
BTGmoderatorDC wrote:Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000
We can create the following equation in which n = total sales:

20,000 + 0.1(n - 80,000) = 30,000 + 0.05n

0.1n - 8,000 = 10,000 + 0.05n

0.05n = 18,000

n = 18,000/0.05 = 1,800,000/5 = 360,000

Answer: D

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by [email protected] » Sun Aug 05, 2018 6:47 pm
Hi All,

We're told that Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in EXCESS of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only IF they exceed $120,000. We're asked which sales figures would result in EQUAL earnings for both Marta and Sandra. This question can be solved Algebraically or by TESTing THE ANSWERS.

Let's TEST Answer B: $150,000
IF....Martha had $150,000 in sales, her commission would be 10% of $150,000 - $80,000 = $70,000.... a $7,000 commission. However, that would raise her total to just $27,000, which is clearly NOT enough to match Sandra's $30,000 base salary. This answer is TOO SMALL, so we can eliminate Answers A and B, and we know the total sales would have to be a lot bigger.

Answer D: $360,000
IF....Martha had $360,000 in sales, her commission would be 10% of $360,000 - $80,000 = $280,000.... a $28,000 commission and a total pay of $48,000.
Sandra's commission would be 5% of $360,000 = $18,000 and a total pay of $48,000
These two totals match, so this must be the answer.

Final Answer: D

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