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A salesman makes a commission of x percent on the first $2,000 worth

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A salesman makes a commission of x percent on the first $2,000 worth  [#permalink]

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New post 22 Feb 2018, 20:46
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A salesman makes a commission of x percent on the first $2,000 worth of sales in any given month and y percent on all further sales during that month. If he makes $700 from $4,000 of sales in October and he makes $900 from $5,000 of sales in November, what is the value of x ?

(A) 2%

(B) 5%

(C) 10%

(D) 15%

(E) 20%

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A salesman makes a commission of x percent on the first $2,000 worth  [#permalink]

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New post 22 Feb 2018, 22:52
Bunuel wrote:
A salesman makes a commission of x percent on the first $2,000 worth of sales in any given month and y percent on all further sales during that month. If he makes $700 from $4,000 of sales in October and he makes $900 from $5,000 of sales in November, what is the value of x ?

(A) 2%

(B) 5%

(C) 10%

(D) 15%

(E) 20%


If the salesman makes a sale of $z, the commission on this sale is \(\frac{x}{100}*2000 + \frac{y}{100}*(z-2000)\)

Since the salesman made $700 from z=$4000 in October, \(\frac{x}{100}*2000 + \frac{y}{100}*2000 = $700\)
Similarly, the salesman made $900 from z=$5000 in October, \(\frac{x}{100}*2000 + \frac{y}{100}*3000 = $900\)

The equations formed are as follows :

20x + 20y = 700 -> (1) * 3 -> 60x + 60y = 2100 -> (3)
20x + 30y = 900 -> (2) * 2 -> 40x + 60y = 1800 -> (4)

Solving for x, we get 20x = 300 -> x = 15%(Option D)
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A salesman makes a commission of x percent on the first $2,000 worth  [#permalink]

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New post 23 Feb 2018, 00:40
Bunuel wrote:
A salesman makes a commission of x percent on the first $2,000 worth of sales in any given month and y percent on all further sales during that month. If he makes $700 from $4,000 of sales in October and he makes $900 from $5,000 of sales in November, what is the value of x ?

(A) 2%

(B) 5%

(C) 10%

(D) 15%

(E) 20%



x/100 x 2000 + y/100 x (s - 2000)

x/100 x 2000 + y/100 x 2000 = 700

x/100 x 2000 + y/100 x 3000 = 900

i.e 10y = 200 ( subtracted the equation ) y=20%

now substitute y = 20

20x + 400 = 700

x = 300/20 = 15


(D) imo
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A salesman makes a commission of x percent on the first $2,000 worth   [#permalink] 23 Feb 2018, 00:40
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