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21 Jun 2024, 09:35
Kudos
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D
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Difficulty:
35%
(medium)
Question Stats:
77% (01:55) correct
23%
(01:56)
wrong
based on 620
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At a post office last week, 25 percent of the employees were part-time employees and the rest were full-time employees. Each of the part-time employees worked \(\frac{3}{5}\) as many hours as each of the full-time employees last week. The total number of hours worked by the part-time employees last week was what fraction of the total number of hours worked by all of the employees at the post office last week?
A. \(\frac{1}{15}\)
B. \(\frac{1}{9}\)
C. \(\frac{3}{20}\)
D. \(\frac{1}{6}\)
E. \(\frac{1}{5}\)
A. \(\frac{1}{15}\)
B. \(\frac{1}{9}\)
C. \(\frac{3}{20}\)
D. \(\frac{1}{6}\)
E. \(\frac{1}{5}\)
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21 Jun 2024, 09:47
Kudos
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kayze
Since each part time employee worked 3/5 as many hours as each full time employee, we can let the number of hours worked by each full-time employee be 5 and the number of hours of each part-time employee be 3.
Thus, the hours worked by the part-time employees is 1 x 3 = 3 and the total hours worked by all employees is 3 + (3 x 5) = 18.
So, the fracton of all hours worked by part-time employees is 3/18 = 1/6.
Answer: D
General Discussion
21 Jun 2024, 09:56
Kudos
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Here is the way I solved this.
Let p = part-time employees and f = full-time employees. We know that \(p = \frac{f}{3}\) because they are 25% of the total employees while f is 75%, thus \(\frac{25%}{75%} = \frac{1}{3}\).
Now, to find the part-time hours worked in relation to full-time hours worked, we multiply \(\frac{1}{3}\) by \(\frac{3}{5}\) and get \(\frac{1}{5}\).
Note that the answer is not \(\frac{1}{5}\), because it is asking for the fraction of part-time work out of the total number of work by ALL employees, not the ratio between part-time work and full-time work. Thus, we must add part-time work and full-time work. If part-time work is \(\frac{1}{5}\) of full-time work, that means the total work is \(\frac{1}{5} + \frac{5}{5} = \frac{6}{5}\).
Now we divide part-time work by total work: \(\frac{1}{5} / \frac{6}{5} = \frac{1}{6}\)
This might be an unconventional or inefficient way to solve, so if anyone has a better way please share!
Let p = part-time employees and f = full-time employees. We know that \(p = \frac{f}{3}\) because they are 25% of the total employees while f is 75%, thus \(\frac{25%}{75%} = \frac{1}{3}\).
Now, to find the part-time hours worked in relation to full-time hours worked, we multiply \(\frac{1}{3}\) by \(\frac{3}{5}\) and get \(\frac{1}{5}\).
Note that the answer is not \(\frac{1}{5}\), because it is asking for the fraction of part-time work out of the total number of work by ALL employees, not the ratio between part-time work and full-time work. Thus, we must add part-time work and full-time work. If part-time work is \(\frac{1}{5}\) of full-time work, that means the total work is \(\frac{1}{5} + \frac{5}{5} = \frac{6}{5}\).
Now we divide part-time work by total work: \(\frac{1}{5} / \frac{6}{5} = \frac{1}{6}\)
This might be an unconventional or inefficient way to solve, so if anyone has a better way please share!
