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A salesman's income consists of a commission and a base salary o

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A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 14 Jul 2015, 00:05
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A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?

A. $150
B. $245
C. $365
D. $715
E. $730

Kudos for a correct solution.

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Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 14 Jul 2015, 01:52
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Bunuel wrote:
A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?

A. $150
B. $245
C. $365
D. $715
E. $730

Kudos for a correct solution.


Total Money Earned till now = 406+413+420+436+395 = 2070

Total Money to be earned in week to maintain average of 500 = 500*7 = 3500

Additional Money to be earned on remaining two days = 3500-2070 = 1430

Base salary of next two weeks = 350+350 = 700

Remaining money to be earned through commission = 1430-700 = 730
Average Money per weeek to be earned through commission = 730/2 = 365

Answer: Option C
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Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 14 Jul 2015, 07:16
1
Another method is to go by options...

Total Money Earned till now = 406+413+420+436+395 = 2000 approx

- Picking option C first : 715$z
Just by rough estimate you can see the total salary for these 2 weeks is 715*2 + 700 = 2130 ------------- (Total is far more than 3500)

- Picking option B : 245$
Just by rough estimate you can see the total salary for these 2 weeks is 245*2 + 700 = 1190 ------------- (Total is far less than 3500)

The only option in between is C.
Hence C !!
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Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 18 Jul 2015, 04:23
Bunuel wrote:
A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?

A. $150
B. $245
C. $365
D. $715
E. $730

Kudos for a correct solution.


Sum of commission for the seven weeks = 56+63+70+86+45+x+y = 150*7 (500 - 350 = 150)

x+y = 1050 - 320 => x+y = 730

They have asked avg. of x+y => (x+y)/2 = 730/2 = $365.

Option C
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Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 18 Jul 2015, 11:36
Bunuel wrote:
A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?

A. $150
B. $245
C. $365
D. $715
E. $730

Kudos for a correct solution.


Total weekly income over 5 weeks=$406+$413+$420+$436+$395=$2070
For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500
Now, $3500-$2070=$1430
From this, we subtract base salary for 2 weeks i.e $350*2=$700
Therefore, commission=$1430-$700=$730 for 2 weeks
Avg weekly commission=$365
Answer C
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Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 19 Jul 2015, 12:30
Bunuel wrote:
A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?

A. $150
B. $245
C. $365
D. $715
E. $730

Kudos for a correct solution.


800score Official Solution:

We need to do this problem step-by-step.

First, we add up the total income amounts for the past 5 weeks:
$406 + $413 + $420 + $436 + $395 = $2070.

To average $500 over 7 weeks, the salesman would need to earn:
$500 × 7 = $3500.

Subtract $2070 from $3500 to determine how much he would need to earn, in total, over the next 2 weeks to average $500 for the 7 weeks:
$3500 – $2070 = $1430.

Since he will earn $700 in base salary over the next two weeks, the commission he must earn in the next two weeks is:
$1430 – $700 = $730.

This is an average of $730/2 = $365 per week for these two weeks.

The correct answer is choice (C).
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Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 20 Jul 2015, 16:19
We are looking for a 7 week average total income of $500 per week, or $150 plus $350 base.

The question does not ask about the base, so it can be ignored for now.

7 weeks * $150/week = $1,050

5 week commissions leading are 56+63+70+86+45 = $320

Total required - Earned so far = $1,050 - $320 = $730

Weeks remaining is 2, therefore commission required per week is $365
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Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 15 Aug 2015, 08:49
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Mascarfi wrote:
A salesman's income consists of two components: commission and regular salary. His salary is $350 a week, and his goal is to make enough money from commissions to average $500 in total income per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What does he need to average (arithmetic mean) in commission income per week, over the next two weeks, to raise his average weekly income to $500 over the 7-week period?

A. $150
B. $245
C. $365
D. $715
E. $730


Total of the 5 weeks = 406+413+420+436+395 = 2070.

Total for the entire 7 week period = 500*7 = 3500

Thus the 2 remaining income totals = 3500-2070 = 1430, per week income total = 1430/2 = 715.

So per week he needs to have an income total of = 715$ out of which 350 is his base income. Thus the commission = 715-350 = 365$. C is the correct answer.
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Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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New post 09 Apr 2016, 18:11
Bunuel wrote:
A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?

A. $150
B. $245
C. $365
D. $715
E. $730

Kudos for a correct solution.


average for 7 weeks 500. total must be 3500
now, last 2 weeks base salary 350x2=700$
406+413=819
420+436=856
819+856=1675+395 = 2070.
2070+700=2770. sum for $ received first 5 weeks + base salary last 2 weeks
3500-2770=730 - must make in commission in last 2 weeks.
730/2 = 365 average commission/week must have

C
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Re: A salesman's income consists of a commission and a base salary o &nbs [#permalink] 09 Apr 2016, 18:11
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