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A salesman's income consists of a commission and a base salary of $350

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A salesman's income consists of a commission and a base salary of $350  [#permalink]

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New post 29 Dec 2014, 08:58
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Question Stats:

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Tough and Tricky questions: Word Problems.



A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 7-week period?

A. $570
B. $586
C. $630
D. $686
E. $715

Kudos for a correct solution.

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Re: A salesman's income consists of a commission and a base salary of $350  [#permalink]

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New post 29 Dec 2014, 10:28
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Before we look at what the salesman actually earned, let's think about how high the total income needs to be for the 500$ average he wants to reach. Over a seven-week period and an average of $500, the total income needs to be $3500 or higher.
In the past 5 weeks, the salesperson earned a total of $2070. That means that in the last 2 weeks, the salesman needs to earn the remaining $1430, or -in average- $715 per week. Answer E.
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Re: A salesman's income consists of a commission and a base salary of $350  [#permalink]

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New post 30 Dec 2014, 10:55
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 7-week period?

A. $570
B. $586
C. $630
D. $686
E. $715

Kudos for a correct solution.



Total of first 5 weeks = $2070
Expected total after seven weeks = 7*500 = $3500

Last two weeks income must be 3500-2070 = $1430 so that average of 7 weeks will be 500

Average last two weeks = 1430/2 = $715
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Re: A salesman's income consists of a commission and a base salary of $350  [#permalink]

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New post 30 Dec 2014, 20:14
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Answer = E. $715

Total 5 week's income = 400*5 + 36+19+20+36-5 = 2070

Setting up the equation

Say "x" is the mean for the 2 months to achieve 500 average for 7 weeks

\(\frac{2070 + 2x}{7} = 500\)

2x = 3500-2070 = 1430

x = 715
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Re: A salesman's income consists of a commission and a base salary of $350  [#permalink]

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New post 08 Jan 2015, 08:17
Bunuel wrote:

Tough and Tricky questions: Word Problems.



A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 7-week period?

A. $570
B. $586
C. $630
D. $686
E. $715

Kudos for a correct solution.


OFFICIAL SOLUTION:

(E) First, we need to add up the wages over 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.

Dividing $1430 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $1430/2 = $715.

The correct answer is choice (E).
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Re: A salesman's income consists of a commission and a base salary of $350  [#permalink]

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New post 02 Jul 2017, 08:45
What i did was to see how can i balance out the total of the shortage of the weekly average from 500 to twice the excess of weekly average of the two unknown weeks.

Therefore, \(105+64+80+87+94=430\)
It clearly shows that Option E having a \(215\) excess income will serve the point. \(2*215=430\)

Therefore, option E.
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Re: A salesman's income consists of a commission and a base salary of $350  [#permalink]

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New post 02 Jul 2017, 08:55
Bunuel wrote:

Tough and Tricky questions: Word Problems.



A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 7-week period?

A. $570
B. $586
C. $630
D. $686
E. $715

Kudos for a correct solution.

Or, \(406+413+420+436+395+(a+b) = 500*7\)
Or, \(2070 + (a+b) = 3500\)
Or, \(a + b = 1430\)

Thus, average of a + b will be \(\frac{1430}{2} = 715\)

Hence, the correct answer must be (E) 715
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Re: A salesman's income consists of a commission and a base salary of $350  [#permalink]

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Re: A salesman's income consists of a commission and a base salary of $350   [#permalink] 27 Oct 2018, 12:27
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