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:

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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 valuesLet Week 1 number of videos sold,

n = 6Let Week 1 average price of video,

z = $20Week 2 number of videos sold is (n-4),

n = 2Week 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 110A) 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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The only thing more dangerous than ignorance is arrogance.

-- Albert Einstein