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Paul sells encyclopedias door-to-door. He earns $160 on ever

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Paul sells encyclopedias door-to-door. He earns $160 on ever  [#permalink]

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New post Updated on: 22 Jan 2014, 06:15
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A
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Question Stats:

72% (01:55) correct 28% (01:51) wrong based on 128 sessions

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Paul sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:

Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->

He does not earn "double commission." That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.

His largest paycheck of the year was $1,320. What were his sales for that pay period?

A)13,200
B)14,800
C)16,400
D)15,800
E)19,600

Originally posted by guerrero25 on 20 Jan 2014, 21:16.
Last edited by guerrero25 on 22 Jan 2014, 06:15, edited 1 time in total.
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Re: Paul sells encyclopedias door-to-door.  [#permalink]

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New post 20 Jan 2014, 22:00
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guerrero25 wrote:
Paul sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:


Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->


He does not earn "double commission." That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.

His largest paycheck of the year was $1,320. What were his sales for that pay period?




A)13,200

B)14,800

C)16,400

D)15,800

E)19,600

I will post the OA soon


His pay check was $1320.
Out of this, $160 was his fixed salary so the total commission he earned was $1320 - $160 = $1160
He earns 10% on the sales of first $10,000 which gives a commission of $1000.
He earns 5% on every subsequent dollar. Since he earns another $160, he must have had sales of another 160*(100/5) = 3200
So his total sales must have been $10,000 + $3200 = $13,200
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Re: Paul sells encyclopedias door-to-door. He earns $160 on ever  [#permalink]

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New post 22 Jan 2014, 00:11
Paul sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn "double commission." That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period?


Using the equation y = mx + C, where, y = Paycheck amount; x= amount of sales exceeding $10000; m = 5% or 1/20; C = 160 + 10000(1/10) = 1160;

\(1320 = \frac{x}{20} + 1160\)

Or,\(x = (1320-1160)(20) = 3200\)

So, Total sales \(= 10000+3200=13200\)

Answer: (A)
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Paul sells encyclopedias door-to-door. He earns $160 on ever  [#permalink]

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New post 26 Aug 2018, 18:31
1
guerrero25 wrote:
Paul sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:

Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->

He does not earn "double commission." That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.

His largest paycheck of the year was $1,320. What were his sales for that pay period?

A)13,200
B)14,800
C)16,400
D)15,800
E)19,600

Paycheck = fixed pay + commissions
\($1,320 = $160\) + commissions
\($(1,320 -160)=$1,160\) in commissions

All of the answer choices are greater than $10,000

\(x=\) first $10,000 in sales
\(y\) = sales amount after the first $10,000
\(x+y=\) total sales amount
\(.10x + .05y=\) total commissions amount

\(.10x+.05y=$1,160\)

\(.10($10,000)+.05(y)=$1,160\)
\($1,000+0.05y=$1,160\)
\(.05y=$160\)

\(y=\frac{$160}{.05}=\frac{$16,000}{5}=$3,200\)

Total sales = \((x+y)=$(10,000+3,200)=$13,200\)

Answer A
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Re: Paul sells encyclopedias door-to-door. He earns $160 on ever  [#permalink]

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New post 12 Nov 2018, 07:22
guerrero25 wrote:
Paul sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:

Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->

He does not earn "double commission." That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.

His largest paycheck of the year was $1,320. What were his sales for that pay period?

A)13,200
B)14,800
C)16,400
D)15,800
E)19,600



Since he earns $160 as base salary and 10% of $10,000 is $1,000, if he sells no more than $10,000 worth of encyclopedias, the maximum he earns is $1,160. However, since he earns $1,320, he must have sold more than $10,000 worth of encyclopedias. Therefore, if we let x = his sales for the paycheck of $1,320, we can create the equation:

160 + 0.1(10,000) + 0.05(x - 10,000) = 1,320

160 + 1,000 + 0.05x - 500 = 1,320

660 + 0.05x = 1,320

0.05x = 660

x = 13,200

Answer: A
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Re: Paul sells encyclopedias door-to-door. He earns $160 on ever  [#permalink]

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New post 13 Nov 2018, 11:15
Hi All,

We're told that Paul sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells and a commission as follows:

10% on the first $10,000.00 and 5% for any additional sales beyond that.

His largest paycheck of the year was $1,320. We're asked for his sales for that pay period. This question can be approached in a couple of different ways. Based on the given answer choices, we can take advantage of a couple of built-in patterns and avoid some of the extra 'math steps.'

To start, we can see that all of the answers are ABOVE $10,000, so we know that part of his commissions was 10% of $10,000 = $1,000. Paul received $160 on top of that piece of his commission, so we have accounted for $1,160. Now, we just have to account for the extra $1320 - $1160 = $160 he earned...

That extra commission was based on 5% of the sales ABOVE $10,000.
5% of $1,000 = $50
$160 is a little more than (3)($50), so the extra sales had to be a little more than (3)($1000). Thus, his total sales for that period were a LITTLE MORE than $10,000 + $3000 = $13,000...

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Re: Paul sells encyclopedias door-to-door. He earns $160 on ever &nbs [#permalink] 13 Nov 2018, 11:15
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