jeepsdaddy wrote:
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8
The easiest way to solve this question is to choose convenient values for the number of day workers and for the number of boxes loaded by each day worker.
We are given that the night crew loaded 3/4 as many boxes as each worker on the day crew and that the night crew has 4/5 as many workers as the day crew. We can set up an equation relating the number of day workers and the number of night workers:
4/5(number of day workers) = number of night workers
Let's choose the convenient value of 20 for the number of day workers and substitute it into the equation above:
4/5 x 20 = number of night workers
16 = number of night workers
Next, we set up the equation for the number of boxes loaded by each worker.
(¾) x (number of boxes loaded by each day worker) = number of boxes loaded by each night worker
Now let's choose the convenient value of 8 for the number of boxes loaded by each day worker and substitute it into the above equation:
¾ x 8 = number of boxes loaded by each night worker
6 = number of boxes loaded by each night worker
Thus, the total number of boxes loaded by each type of worker is as follows:
Day workers = 20 x 8 = 160
Night workers = 16 x 6 = 96
Total boxes loaded = 160 + 96 = 256
The question asks us to determine the fraction of all the boxes loaded by the day crew, and that is:
(Total boxes loaded by day crew)/(Total boxes loaded)
160/256
40/64
5/8
Answer is E.
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