Algebra: Applied Problems

Question

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

Answer: the workers on the night crew will load 3/4(4/5)=3/5 as many boxes as the day crew. Total loaded by both day and night crews is thus 1+3/5=8/5 of the day crew's work. Therefore 1/(8/5)=5/8 or E.

This is the answer given by the OG 11th edition. Can someone work this problem in a different way because I don't understand the explanation.

GMATGuruNY · Answer

tvd04c 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

Answer: the workers on the night crew will load 3/4(4/5)=3/5 as many boxes as the day crew. Total loaded by both day and night crews is thus 1+3/5=8/5 of the day crew's work. Therefore 1/(8/5)=5/8 or E.

This is the answer given by the OG 11th edition. Can someone work this problem in a different way because I don't understand the explanation.

Let the number of day crew workers = 5.
Then the number of night crew workers = 4/5 * 5 = 4.

Let the number of boxes loaded by each day crew worker = 4.
Then the number of boxes loaded by each night crew worker = 3/4 * 4 = 3.

Total boxes loaded by the day crew = 5*4 = 20.
Total boxes loaded by the night crew = 4*3 = 12.
Day crew boxes/Total boxes = 20/(20+12) = 20/32 = 5/8.

The correct answer is E.

manpsingh87 · Answer

tvd04c 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

Answer: the workers on the night crew will load 3/4(4/5)=3/5 as many boxes as the day crew. Total loaded by both day and night crews is thus 1+3/5=8/5 of the day crew's work. Therefore 1/(8/5)=5/8 or E.

This is the answer given by the OG 11th edition. Can someone work this problem in a different way because I don't understand the explanation.

Let the number of day crew workers = 5.
Then the number of night crew workers = 4/5 * 5 = 4.

Let the number of boxes loaded by each day crew worker = 4.
Then the number of boxes loaded by each night crew worker = 3/4 * 4 = 3.

Total boxes loaded by the day crew = 5*4 = 20.
Total boxes loaded by the night crew = 4*3 = 12.
Day crew boxes/Total boxes = 20/(20+12) = 20/32 = 5/8.

The correct answer is E.

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