Each week, a clothing salesperson receives a commission equal

Video solution from Quant Reasoning:

The commision that the salesperson will receive for that week is 500*0.15+(x-500)*0.2, where x is the salesperson's sales above $500. So, 500*0.15+(1300-500)*0.2=75+160=$235

The correct answer is C.

The slabs for computing the commision on the sales of x are as follows:
1. 15% on the first $500 in sales. \(0.15*$500 = $75\) when x > $500
2. 20$ on the remaining amount (x - $500) where x is the total sales amount.

The total commision is \(75 + 0.20.2(x - 500) = 75 + 0.2x - 100 = 0.2x - 25\)

Given: Weekly sales of the clothing salesperson is $1300(Here, x = $1300)

Therefore, the total commission received by the clothing salesperson is \(0.2x - 25 = 260 - 25 =\) $235(Option C)

Solution

Given:

• A salesperson receives a commission equal to 15 percent of the first $500 in sales and 20 percent of all additional sales that week

To find:

• The commission the salesperson received on a sale of $1300 in a week

Approach and Working:

• Commission for first $500 sale = 15% of $500 = $75
• Commission for the remaining sale = 20% of ($1300 - $500) = 20% of $800 = $160
• Therefore, total commission = $75 + $160 = $235

Hence, the correct answer is option C.

Answer: C
_________________

1) Amount earned on sales = $500

For the first $500 in sales (of the total $1,300 in sales), the salesperson earns 15%
\((.15*$500)=$75\)
Earned so far: $75

2) Amount earned on rest of sales = $800

Remaining sales on which she earns 20% commission? ($1,300 - $500) = $800

She earns 20% on that amount:
\((.20*$800)=$160\)
Second amount earned: $160

Total amount earned: ($75 + 160) = $235

Answer C
_________________

We can express the solution as:

0.15 x 500 + 0.2(1300 - 500) = 75 + 160 = 235

Answer: C
_________________

[1] Equation

Where x >= 500

500 * 15% + (x - 500) * 20%

= 75 + (x - 500) * 20%

[2] Solve

x = 1300

75 + (1300 - 500) * 20%

= 75 + 800 * 20%

= 75 + 160

= 235

15% of 1st 500 sale = 75$
remaining ( 1300-500) $ = 800$

Now he is getting 20% of 800$ = 160$

So in total commission = 160+75= 235 $

Each week, a clothing salesperson receives a commission equal to 15 percent of the first $500 in sales and 20 percent of all additional sales that week.
15% * $500 = $75

What commission would the salesperson receive on total sales for the week of $1,300 ?
$1300 - $500 = $800
20% * $800 = $160

Total commission = $75 + $160 = $235

IMO C

\(\frac{15}{100}*500 + \frac{20}{100*800} = 75 + 160 = 235\), Amswer will be (C)
_________________

Answer: Option C

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

Many algebra questions at the GMAT have an equation that is the multiplication of quantity x average value.
GMAT is about to recognize patterns. The pattern recognition gives you speed.

_________________

BrentGMATPrepNow, Hi Brent, could you advise why this formula 500*0.15+(x-500)*0.2 = 1300 not getting the right answer? Thanks

I'll answer your question with another question: In your equation, 500*0.15+(x-500)*0.2 = 1300, what does x represent?

Presumably, x = the total sales, which means 500*0.15+(x-500)*0.2 represents the total commission the salesman will receive on x dollars worth of sales.
In other words, 500*0.15+(x-500)*0.2 = the total commission the salesman will receive on x dollars worth of sales.

Since the question tells us that the salesperson had $1300 in total sales, all you need to do is replace x with 1300 in your equation.
We get: 500*0.15 + (1300-500)*0.2 = the total commission the salesman will receive on x dollars worth of sales.
Simplify: $75 + $160 = the total commission the salesman will receive on x dollars worth of sales.
In other words, $235 the total commission the salesman will receive on x dollars worth of sales.
Answer: C

Great explanation thanks BrentGMATPrepNow, so the issue here is I've repeated total sales twice here ...

That's right.
Once you create the equation 500*0.15 + (1300-500)*0.2 = the total commission the salesman will receive on x dollars worth of sales., all you need to do is replace x with 1300 in your equation.

Sure thanks BrentGMATPrepNow and noted.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________