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

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
A salesman's income consists of a commission and a base salary o  [#permalink]

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14 Jul 2015, 00:05
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Difficulty:

45% (medium)

Question Stats:

74% (02:40) correct 26% (02:46) wrong based on 94 sessions

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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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14 Jul 2015, 01:52
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1
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

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

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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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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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Posts: 661
Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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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
Math Expert
Joined: 02 Sep 2009
Posts: 53020
Re: A salesman's income consists of a commission and a base salary o  [#permalink]

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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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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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15 Aug 2015, 08:49
1
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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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
Re: A salesman's income consists of a commission and a base salary o   [#permalink] 09 Apr 2016, 18:11
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