Martha receives an annual salary of $20,000 plus a commission of 10 pe

Question

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

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000

niks18 · Answer

Let  S  be the sale when both the salaries are equal

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

Solving we get  S=360000

Option  D

JeffTargetTestPrep · Answer

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/.05 = 360,000

Answer: C

niks18 · Answer

Hi  JeffTargetTestPrep

5% commission is on total sales. So the second equation should be 0.5n

Posted from my mobile device

JeffTargetTestPrep · Answer

Good call!

My solution has been amended.

rocko911 · Answer

I understood the equation methodology but If I do it simply by calculating then why is C coming out as an answer?

Let C = 240, 000 be an answer

for Martha = 20,000 + (10/100 ) * (240,000 - 80,000)

= 36,000

for Sandra = 30,000 + (5/100) * (240,000 - 120,000)

= 36,000

THEN WHY IS C wrong? please help

Bunuel · Answer

Check the highlighted part: 5% from TOTAL annual sales.

For 240, 000 Sandra gets 30,000 + (5/100)*240,000 = 42,000.

rocko911 · Answer

Thanks ...i totally ignored that part...got it now

rahul16singh28 · Answer

Let  x be the total sales.

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

0.05x = 18,000

x = 360,000

rmahe11 · Answer

Umm why is A not correct ? Let's say if its 100000 then Martha will get 20000+ 0.1 of 100000 which is equal = 30000 , while sandra has a fixed salary of 30000 and 5 percent commision on sales if it exceeds 120k which is not hence salary will be 30000 and hence they are equal ?

Bunuel · Answer

The stem specifies that Martha receives 10 percent on sales in excess of $80,000, which means she only earns commission on sales made after the first $80,000. Here's how it breaks down:

For $100,000, Martha would receive $20,000 + 10% of ($100,000 - $80,000) = $20,000 + $2,000 = $22,000. 
 For $100,000, Sandra would receive $30,000 only, as her sales do not meet the $120,000 threshold for commission.

This highlights why A is not the correct answer.

Martha receives an annual salary of $20,000 plus a commission of 10 pe

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Martha receives an annual salary of $20,000 plus a commission of 10 pe

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