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At a local office, each trainee can stuff 2/3 as many envelopes per
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03 Jan 2016, 12:58
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At a local office, each trainee can stuff 2/3 as many envelopes per day as a full time worker. If there are \(\frac{2}{5}\) as many trainees as there are full time workers, then what fraction of all the envelopes stuffed in a day did the trainees stuff?
A. 2/19
B. 2/17
C. 4/19
D. 4/17
E. 14/15
A. 2/19
B. 2/17
C. 4/19
D. 4/17
E. 14/15
Re: At a local office, each trainee can stuff 2/3 as many envelopes per
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04 Jan 2016, 14:13
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To know the fraction of all envelopes stuffed by trainees, we need to know how many envelopes were stuffed by trainees and how many were stuffed in total.
let \(x=\)number of envelopes a full-time worker can stuff in a day
Then the number of envelopes a trainee can stuff in a day is \(\frac{2}{3}x\)
(Note that we don't really need the variable, but for visualization purposes, it can sometimes make it easier to understand and follow what is going on.)
It is given that the number of trainees to full-time workers is 2:5, and since we are only concerned with the ratio envelopes stuffed by trainees, then we can assume that there are 5 full time workers and 2 trainees.
Total number of envelopes stuffed = (all envelopes stuffed by full-time workers) + (all envelopes stuffed by trainees)
\(T=5x + 2*\frac{2}{3}x\)
What we're asked to find is the fraction of envelopes stuffed by trainees =
(all envelopes stuffed by trainees)/(Total amount of envelopes stuffed) =
\(=\frac{(2*\frac{2}{3}x)}{(5x+2*\frac{2}{3}x)}\)
\(= \frac{\frac{4}{3}x}{\frac{19}{3}x}\)
\(=\frac{4}{19}\)
Answer: C
let \(x=\)number of envelopes a full-time worker can stuff in a day
Then the number of envelopes a trainee can stuff in a day is \(\frac{2}{3}x\)
(Note that we don't really need the variable, but for visualization purposes, it can sometimes make it easier to understand and follow what is going on.)
It is given that the number of trainees to full-time workers is 2:5, and since we are only concerned with the ratio envelopes stuffed by trainees, then we can assume that there are 5 full time workers and 2 trainees.
Total number of envelopes stuffed = (all envelopes stuffed by full-time workers) + (all envelopes stuffed by trainees)
\(T=5x + 2*\frac{2}{3}x\)
What we're asked to find is the fraction of envelopes stuffed by trainees =
(all envelopes stuffed by trainees)/(Total amount of envelopes stuffed) =
\(=\frac{(2*\frac{2}{3}x)}{(5x+2*\frac{2}{3}x)}\)
\(= \frac{\frac{4}{3}x}{\frac{19}{3}x}\)
\(=\frac{4}{19}\)
Answer: C
At a local office, each trainee can stuff 2/3 as many envelopes per
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07 Jan 2016, 03:11
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My answer is C.
Simple solution is considered Full time and trainee employees separately. We have a table:
We plugged in the number of full time employees is 5.
No of people | Work rate | Time(1 day) | The amount of work
Trainee 2 | 2/3 | 1 | 4/3
Full time 5 | 1 | 1 | 5
|
The fraction amount of work done by trainee to total: 4/3 : (4/3+5) = 4/19.
Simple solution is considered Full time and trainee employees separately. We have a table:
We plugged in the number of full time employees is 5.
No of people | Work rate | Time(1 day) | The amount of work
Trainee 2 | 2/3 | 1 | 4/3
Full time 5 | 1 | 1 | 5
|
The fraction amount of work done by trainee to total: 4/3 : (4/3+5) = 4/19.