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During the first week in May, a video salesman sold n videos at an ave

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Bunuel
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During the first week in May, a video salesman sold n videos at an ave [#permalink] New post   02 Jan 2018, 01:27
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A
B
C
D
E

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15% (low)

Question Stats:

88% (01:55) correct 12% (01:07) wrong based on 33 sessions
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During the first week in May, a video salesman sold n videos at an average (arithmetic mean) commission of z dollars per video. During the next week, the same salesman sold n – 4 videos at an average commission of $15 less than the week before. What is the difference in total commissions from the first week to the second week in terms of n and z?

A. nz – 60
B. n^2 – z + 60
C. 2nz – 15z +60
D. 4z + 15n – 60
E. 4z + 60
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D
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Re: During the first week in May, a video salesman sold n videos at an ave [#permalink] New post   02 Jan 2018, 11:19
I solved this by trial and error method

Lets say that first week the salesman sells 10 videos at 35$ commission.
first week = 350$ commission

second week 6 videos at 20$ commission
second week = 120$ commission

difference = 350 - 120 = 230$

we took n = 10 and z = 35

Try to check with all the options

the correct answer is D (4*35 + 15*10 - 60 = 230)
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generis
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During the first week in May, a video salesman sold n videos at an ave [#permalink] New post   02 Jan 2018, 12:34
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Bunuel wrote:
During the first week in May, a video salesman sold n videos at an average (arithmetic mean) commission of z dollars per video. During the next week, the same salesman sold n – 4 videos at an average commission of $15 less than the week before. What is the difference in total commissions from the first week to the second week in terms of n and z?

A. nz – 60
B. n^2 – z + 60
C. 2nz – 15z +60
D. 4z + 15n – 60
E. 4z + 60

Attachment:
AnScommissions.png
AnScommissions.png [ 17.5 KiB | Viewed 1370 times ]

Algebra
\(A*n = S\)

• Week 1
A = z
n = n
SUM = nz

• Week 2
A = (z - 15)
n = (n - 4)
SUM = (n - 4)(z - 15)

For Week 2 SUM, multiply terms A*n
(n - 4)(z - 15)
SUM = (nz - 25n - 4z + 60)

• DIFFERENCE between Week 1 SUM and Week 2 SUM?
nz - (nz - 25n - 4z + 60) =
nz - nz + 25n + 4z - 60 =
25n + 4z - 60, or
4z + 25n - 60

Answer D

Assign values

Let Week 1 number of videos sold, n = 6
Let Week 1 average price of video, z = $20
Week 2 number of videos sold is (n-4), n = 2
Week 2 average price per video is (z-15), ($20 - 15) = z = $5

• Week 1 SUM, where A*n = S
($20 * 6) = $120

• Week 2 SUM
($5 * 2) = $10

• Difference between Week 1 sum and Week 2 sum:
$120 - 10 = $110

• Using n = 6, z = 20, find the answer choice that yields 110

A) nz – 60
120 - 60 = $60. NOT A MATCH

B) n^2 – z + 60
36 - 20 + 60 = 76. NOT A MATCH

C) 2nz – 15z +60
2(120) - (15)(20) + 60
240 - 300 + 60 = 0. NOT A MATCH

D) 4z + 15n – 60
80 + 90 - 60 = 110. MATCH

E) 4z + 60
80 + 60 = 140. NOT A MATCH

Answer D
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During the first week in May, a video salesman sold n videos at an ave [#permalink] New post   02 Jan 2018, 13:31
I got D answer by taking sample values and then poe. Is there any easy way please for this Bunuel


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Re: During the first week in May, a video salesman sold n videos at an ave [#permalink] New post   12 Aug 2018, 23:39
generis wrote:
Bunuel wrote:
During the first week in May, a video salesman sold n videos at an average (arithmetic mean) commission of z dollars per video. During the next week, the same salesman sold n – 4 videos at an average commission of $15 less than the week before. What is the difference in total commissions from the first week to the second week in terms of n and z?

A. nz – 60
B. n^2 – z + 60
C. 2nz – 15z +60
D. 4z + 15n – 60
E. 4z + 60

Attachment:
AnScommissions.png

Algebra
\(A*n = S\)

• Week 1
A = z
n = n
SUM = nz

• Week 2
A = (z - 15)
n = (n - 4)
SUM = (n - 4)(z - 15)

For Week 2 SUM, multiply terms A*n
(n - 4)(z - 15)
SUM = (nz - 25n - 4z + 60)

• DIFFERENCE between Week 1 SUM and Week 2 SUM?
nz - (nz - 25n - 4z + 60) =
nz - nz + 25n + 4z - 60 =
25n + 4z - 60, or
4z + 25n - 60

Answer D

Assign values

Let Week 1 number of videos sold, n = 6
Let Week 1 average price of video, z = $20
Week 2 number of videos sold is (n-4), n = 2
Week 2 average price per video is (z-15), ($20 - 15) = z = $5

• Week 1 SUM, where A*n = S
($20 * 6) = $120

• Week 2 SUM
($5 * 2) = $10

• Difference between Week 1 sum and Week 2 sum:
$120 - 10 = $110

• Using n = 6, z = 20, find the answer choice that yields 110

A) nz – 60
120 - 60 = $60. NOT A MATCH

B) n^2 – z + 60
36 - 20 + 60 = 76. NOT A MATCH

C) 2nz – 15z +60
2(120) - (15)(20) + 60
240 - 300 + 60 = 0. NOT A MATCH

D) 4z + 15n – 60
80 + 90 - 60 = 110. MATCH

E) 4z + 60
80 + 60 = 140. NOT A MATCH

Answer D




Hi,

Thanks for your explanation,

Shouldn't the development of week 2 read 15 instead of 25?

For Week 2 SUM, multiply terms A*n
(n - 4)(z - 15)
SUM = (nz - 25n - 4z + 60)

Thanks
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Re: During the first week in May, a video salesman sold n videos at an ave [#permalink] New post   03 Jun 2020, 22:03
IMO(D)

$z = cost of video
n = no. of video


Diff in commission = n*z - (n-4)*(z-15)
= n*z - [ n*z - 15*n - 4*n + 15*4 ]
= 15n + 4z - 15*4
= 15n + 4z- 60
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Re: During the first week in May, a video salesman sold n videos at an ave [#permalink]
03 Jun 2020, 22:03
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