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A construction company that employs 1,500 non-union free-lance workers

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A construction company that employs 1,500 non-union free-lance workers  [#permalink]

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New post 25 Jan 2018, 23:46
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A
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E

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  45% (medium)

Question Stats:

40% (01:44) correct 60% (03:34) wrong based on 27 sessions

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A construction company that employs 1,500 non-union free-lance workers pays each of these workers $8 per hour for the first 50 hours worked during a week and x percent more than that rate for hours worked in excess of 50. If the total payroll for the non-union workers at the end of a week in which 20 percent of them worked 20 hours, 50 percent worked 40 hours, and the rest worked 80 hours, is $630,000 what is x?

A. 10
B 20
C. 25
D. 40
E. 50

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Re: A construction company that employs 1,500 non-union free-lance workers  [#permalink]

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New post 26 Jan 2018, 20:52
Cost for the first 50 hrs = 8$/hr
For the hrs worked after 50 hrs = (1 + x/100)*8/hr

0.2 * y * 160 + 0.5 * y * 320 + 0.3 * y * 400 + 0.3 * y * 8 * 30 (1 + x/100) = 63 * 10^4
32y + 160y + 120y + 72y(1 + x/100) = 63 * 10^4
72y(1 + x/100) = (630*10^3 - 468 * 10^3)
(1 + x/100) = (162 * 10^3)/(72 * 1500)
(1 + x/100) = 1.5
x = 50

Answer: E
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Re: A construction company that employs 1,500 non-union free-lance workers  [#permalink]

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New post 26 Jan 2018, 23:37
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Bunuel wrote:
A construction company that employs 1,500 non-union free-lance workers pays each of these workers $8 per hour for the first 50 hours worked during a week and x percent more than that rate for hours worked in excess of 50. If the total payroll for the non-union workers at the end of a week in which 20 percent of them worked 20 hours, 50 percent worked 40 hours, and the rest worked 80 hours, is $630,000 what is x?

A. 10
B 20
C. 25
D. 40
E. 50


As per the question, we get

\(300 Workers -- 20 hours each -- 8*20*300 = 48,000\)
\(750 Workers -- 50 Hours Each -- 8*50*750 = 240,000\)
\(450 Workers -- 80 Hours Each -- 8*450*50 + 8*450*30*(1+\frac{x}{100})\)

\(630,000 = 48,000+240,000 + 180,000 + 108,000*(1+\frac{x}{100})\)

\(x = 50\)
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Re: A construction company that employs 1,500 non-union free-lance workers  [#permalink]

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New post 29 Jan 2018, 11:04
Bunuel wrote:
A construction company that employs 1,500 non-union free-lance workers pays each of these workers $8 per hour for the first 50 hours worked during a week and x percent more than that rate for hours worked in excess of 50. If the total payroll for the non-union workers at the end of a week in which 20 percent of them worked 20 hours, 50 percent worked 40 hours, and the rest worked 80 hours, is $630,000 what is x?

A. 10
B 20
C. 25
D. 40
E. 50


We see that 0.2 x 1500 = 300 workers worked 20 hours, 750 worked 40 hours and 1500 - 300 - 750 = 450 worked 80 hours.

We can create the equation:

(300)(8)(20) + (750)(8)(40) + (450)(8)(50) + (450)[(100 + x)/100](8)(30) = 630,000

48,000 + 240,000 + 180,000 + 108,000[(100 + x)/100]= 630,000

108,000[(100 + x)/100] = 162,000

108[(100 + x)/100] = 162

10,800 + 108x = 16,200

108x = 5,400

x = 50

Answer: E
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Re: A construction company that employs 1,500 non-union free-lance workers   [#permalink] 29 Jan 2018, 11:04
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