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PS problem! please help

by dqure040 » Thu Oct 22, 2015 7:50 am
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 2 crews did the day crew load?
a) 1/2, b) 2/5, C) 3/5 d) 9/5 E) 5/8

I'm having a hard time visualizing this question. If N=night crew and D=day crew, i understand N=3/4D, but then I don't follow
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by DavidG@VeritasPrep » Thu Oct 22, 2015 8:06 am
dqure040 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 2 crews did the day crew load?
a) 1/2, b) 2/5, C) 3/5 d) 9/5 E) 5/8

I'm having a hard time visualizing this question. If N=night crew and D=day crew, i understand N=3/4D, but then I don't follow
Pick some simple numbers to make the problem concrete. Say, each worker on the night crew loaded 3 boxes and each worker on the day crew loaded 4 boxes. (So we have our 3/4 ratio.)

And say we have have 4 night crew workers and 5 day crew workers, to give us our 4/5 ratio.

If 4 night crew works load 3 boxes each, they load a total of 3*4 = 12 boxes.
If 5 day crew works, load 4 boxes each, the load a total of 5*4 = 20 boxes.
The total boxes loaded = 12 + 20 = 32.

The day crew loaded 20 of 32 boxes or 20/32 = 5/8.
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by [email protected] » Thu Oct 22, 2015 10:04 am
HI dqure040,

TESTing VALUES (the approach that David used) is a fairly easy way to work through this question. If you want to use an Algebraic approach, then that's fine, but you have to be very careful about what your variables represent. I'm going to give you some help in setting up the 'terms' so that you can reattempt the Algebra on your own...

The number of night workers is related to the number of day workers, but NOT the way that you wrote your equation.

IF...
N = number of night workers
D = number of day workers

N = (4/5)D

Next, you have to create a variable and an equation for the number of boxes loaded per employee.

B = number of boxes loaded

B = number loaded per day worker
(3/4)B = number loaded per night worker

Using these equations and ideas, what would you do next?

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by dqure040 » Thu Oct 22, 2015 10:25 am
Hi Rich, that's the part I'm having difficulty "visualizing" I understand the 2 ratios, but get to the final ratio with 2 unknowns is my issue.

Filling in numbers, I can see how the solution came to be, but with expressions I can't see it. Normally I'm better with equations, but i guess ratios are a weak point.
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by [email protected] » Thu Oct 22, 2015 10:33 am
Hi dqure040,

This prompt ultimately asks for the fraction of the TOTAL BOXES that were loaded by the DAY workers. Using the information from the last post...

Total boxes loaded by Day workers = (D)(B)
Total boxes loaded by Night workers = (4/5)(D)(3/4)(B) = (12/20)(D)(B)

Total of ALL boxes = (D)(B) + (12/20)(D)(B) = (32/20)(D)(B)

Fraction loaded by the Day workers = (D)(B)/[(32/20)(D)(B)]

The DBs 'cancel out' and we're left with 1/(32/20) = 20/32 = 5/8

Final Answer: E

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