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16 Jan 2020, 01:49
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D
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Difficulty:
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Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.
(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
16 Jan 2020, 02:03
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For 40 hours, Salary = $20
—> Salary for 1 hour = \(\frac{ 20}{40} = $ 0.5 \)
salary per hour after 40 hours = 1/6 more tuan normal salary = 7/6th of 0.5 = \(\frac{ 7}{6 }*0.5 = $\frac{ 7}{12 } \)
Let the number of hours worked beyond 40 = \( x\)
—> Overtime salary earned = \( 23.5 - 20 = 3.5 \)
—> \(\frac{ 7}{12}* x = 3.5 \)
—> \( x = 3.5* \frac{ 12}{7 } = 6 \) hours
So, total hours worked = 40 + 6 = 46
Option D
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—> Salary for 1 hour = \(\frac{ 20}{40} = $ 0.5 \)
salary per hour after 40 hours = 1/6 more tuan normal salary = 7/6th of 0.5 = \(\frac{ 7}{6 }*0.5 = $\frac{ 7}{12 } \)
Let the number of hours worked beyond 40 = \( x\)
—> Overtime salary earned = \( 23.5 - 20 = 3.5 \)
—> \(\frac{ 7}{12}* x = 3.5 \)
—> \( x = 3.5* \frac{ 12}{7 } = 6 \) hours
So, total hours worked = 40 + 6 = 46
Option D
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16 Jan 2020, 02:32
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We know 40 hours = $20 ... overtime earned - $23.5 - $20 = $3.5
1 hour = $ \(\frac{20}{40}\) = $0.5
Overtime - Salary/hr after 40 hours = 1/6 times the normal salary - \(1 + \frac{1}{6} = \frac{7}{6}\)
We can writes as - \(\frac{7}{6} * 0.5\) = \(\frac{3.5}{6}\)
Let the number of hours worked after 40 hours as x and we already know that overtime earned is $3.5
\(\frac{3.5 * x}{6 } = 3.5\)
x=6
Total time - normal + overtime - 40 + 6 = 46
'D' is the winner
1 hour = $ \(\frac{20}{40}\) = $0.5
Overtime - Salary/hr after 40 hours = 1/6 times the normal salary - \(1 + \frac{1}{6} = \frac{7}{6}\)
We can writes as - \(\frac{7}{6} * 0.5\) = \(\frac{3.5}{6}\)
Let the number of hours worked after 40 hours as x and we already know that overtime earned is $3.5
\(\frac{3.5 * x}{6 } = 3.5\)
x=6
Total time - normal + overtime - 40 + 6 = 46
'D' is the winner
