Need help with word problem

O

onebadd68

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Three workers sort 66 boxes in a day. One of the workers is three times more productive than the second worker and twice as productive as the third worker. How many boxes did the second most productive worker sort?

A. 24
B. 18
C. 10
D. 15
E. 20
 
onebadd68 said:
Three workers sort 66 boxes in a day. One of the workers is three times more productive than the second worker and twice as productive as the third worker. How many boxes did the second most productive worker sort?

A. 24
B. 18
C. 10
D. 15
E. 20
Click to expand...

Start with defining - What needs to be found?

Name it

How many boxes did the second most productive worker sort?

There are three worker - we do not know which one is the most productive - yet. So

Number of boxes the first worker sort = B1

Number of boxes the second worker sort = B2

Number of boxes the third worker sort = B3

Now what......

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
onebadd68 said:
Im totally confused.
Click to expand...

Do you want us to guess why you are confused? That's not very efficient. It would be better for everybody, if you were to begin by explaining why you're stuck or what you've thought about thus far. What grade are you in?

Do you understand the meaning of "second-most productive worker"? Is it worker 1, 2, or 3 -- based on the relative numbers of boxes sorted by each (as given in the exercise).

Try playing with some real numbers, until you understand the ranking of workers 1, 2, and 3. In other words, which worker is the most productive? Is it worker 1, 2, or 3? Which worker is second-most productive? Is it worker 1, 2, or 3?

Once you understand which of the three workers is second-most productive, you may simply try the multiple choices until you find the one that works.
 
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onebadd68 said:
I did try quessing using each number, but nothing comes out to 66.
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Okay -- I now understand that you tried all of the numbers, and nothing worked.

(I just tried the exercise, but I made a mistake at the start. Now, I'm trying again.)

Please show us what you tried.

What grade are you in?
 
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I tell ya -- some exercise wording sure fools me (not hard to do, sometimes). :oops:

Okay -- I got it to work out.

Maybe you are making the same initial error that I did.

So, let's confirm something.

The exercise provides the relationships between the numbers of boxes sorted for three workers: Worker1, Worker2, and Worker3.

Now, are you thinking that Worker2 is the same as "second-most productive worker"?

(That was my initial mistake, DESPITE THE FACT that I already posted to get the rankings straight in your head first. Yikes.)
 
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What equation (where you placed numbers) did you try first?
 
onebadd68 said:
Three workers sort 66 boxes in a day. One of the workers(B1) is three times more productive than the second worker (B2) and twice as productive as the third worker(B3). How many boxes did the second most productive worker sort?

A. 24
B. 18
C. 10
D. 15
E. 20
Click to expand...
There are three worker - we do not know which one is the most productive - yet. So

Number of boxes the first worker sort = B1

Number of boxes the second worker sort = B2

Number of boxes the third worker sort = B3

Three workers sort 66 boxes in a day → B1 + B2 + B3 = 66......................................................... (1)

One of the workers(B1) is three times more productive than the second worker (B2) → B1 = 3 * B2 → B2 = B1/3 ..................... (2)

One of the workers(B1) is twice as productive as the third worker(B3) → B1 = 2 * B3 → B3 = B1/2 ..................... (3)

Replacing B2 and B# from (2) and (3) into (1), we get:

B1 + B1/3 + B1/2 = 66 → B1 = ?? ....................................................................................(4)

Replace B1 from (4) into (2) and (3) and solve for B2 and B3

Now decide who is the second most productive worker, and finish answering the question......
 
onebadd68 said:
Three workers sort 66 boxes in a day. One of the workers is three times more productive than the second worker and twice as productive as the third worker. How many boxes did the second most productive worker sort?

A. 24
B. 18
C. 10
D. 15
E. 20
Click to expand...
Let x be the number of boxes the most productive worker can sort. Since he is "three times more productive than the second worker", the second worker sorts x/3 boxes. Since he is "twice as productive as the third worker", the third worker sorts x/2 boxes. Altogether, they sort 66 boxes in a day: x+ x/3+ x/2= 66. The "common denominator" is 6 so that is 6x/6+ 2x/6+ 3x/6= 11x/6= 66. Solve that equation for x. The aswer to the question, "How many boxes did the second most productive worker sort?", is x/2.

(The "second most productive worker" is the third worker in the problem, not the second worker.)
 
Why can we not simply use arithmetic?

Can the OP multiply a number by 3?

Can the OP divide a number by 2?

I'm not convinced that algebraic methods are appropriate for this poster; my default interpretation of posters on this board tends to be grade-school students. :cool:
 
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