Problem Solving

Problem 151

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

I think the fast way is to plug in some nice numbers.
Since the two pieces of information regarding the night shift are related to the information regarding the day shift, let's assign some nice values to the DAY shift.

Number of workers
Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)

Boxes loaded per worker
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)

Total boxes loaded
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes

Combined total boxes for both shifts = 20 + 12 = 32

Of the 32 boxes, the day shift loaded 20 of them.
20/32 = [spoiler]5/8[/spoiler]

Answer: E

Cheers,
Brent

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

Here's an algebraic solution:

Number of workers
Day shift: Let W = the # of day shift workers
Night shift: There are 4W/5 workers (since 4/5 of W = 4W/5)

Boxes loaded per worker
Day shift: Let B = boxes per worker on day shift
Night shift: So, 3B/4 = boxes per worker on night shift

Total boxes loaded
Day shift: W workers times B boxes per worker = WB boxes
Night shift: 4W/5 workers times 3B/4 boxes per worker = 12WB/20 boxes. Simplify to get a total of 3WB/5 boxes.

Combined total boxes for both shifts = WB + 3WB/5 = 8WB/5

Of the 8WB/5 boxes, the day shift loaded WB of them.
WB/(8WB/5) = 5/8 = E

Cheers,
Brent

didieravoaka wrote:Hi guys,

Does anyone can help me for the problems 151 and 226 in the official guide 13th edition?

Problem 151: I don't understand why we multiply 3/4 by 4/5 and then why we add 1 to 3/5. Another way to solve this problem will help me.
Problem 226: I don't understand why we choose answer D.

Thank you.

Marc.

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
(D) 4/5
(E) 5/8

Solution:

One 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 each worker on 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: E

Note that, in this "fraction of total" question, we could have chosen any realistic values for the number of day workers and for the number of boxes loaded by each day worker. We chose the convenient values of 20 and 8, respectively, but other values would have yielded the same fractional answer.