how many liters...

[Dr.Peterson]

Well, agreed, it is poorly written but it is like that. I have not take anything away or added anything to it either. And I totally agree. It should be each machine doing a dozen daily.
If that's the case, then,
144 machine * 12 bags =1,728 bas that are being manufactured on a daily basis.

Yes, we have to take what we're given (though sometimes you can ask the author, or your official interpreter (your teacher) about it).

Now, the question is:
If one liter of lubricant is needed for to oil 24 machines, how many liters of lubricant are needed to produce a dozen bags?
uhmmm,
any hint?

Take it in small steps. How much lubricant is needed in a day? Then you can look for the next step.

144/24= 6 liters are need to grease all of the machines.

Okay, so it takes 6 liters for 1728 bags ...

 

[eddy2017]

How much lubricant is needed in a day? @#21
What can I do to find how much lube is needed in a single day?
Will I have to divide 1728 into 6 liters?. Will that be a way?.

 

[Dr.Peterson]

How much lubricant is needed in a day? @#21
What can I do to find how much lube is needed in a single day?
Will I have to divide 1728 into 6 liters?. Will that be a way?.

It looks like you're struggling with ratios; you're close, but unsure. A useful way to work with them is to focus on units.

You are asked "how many liters of lubricant are needed to produce a dozen bags?" That means you want "liters per dozen"; which means you want to divide the number of liters by the number of dozen bags. ("Per" can be thought of as meaning "divided by"; that's why we often write it as "/", as in "liters/dozen".)

How many liters in a day? How many dozen bags in a day?

(By the way, I worded my earlier suggestion in terms of the number of dozen rather than a number of bags, in order to help you get past this; but working with bags seems more natural, so keep on this way.)

 

[Steven G]

Hi, dear friends and teacher: I am bringing this problem up before you.

In a factory, 144 machines produce an average of a dozen bags in a day. If one liter of lubricant is needed for the gears of 24 machines, how many liters of lubricant are needed to produce a dozen bags?

Thanks,
eddy

[math] 12 \ bags = 12 \ bags *\dfrac{1 \ machines}{12 \ bags}*\dfrac{1\ liter\ lubricant}{24\ machines}=...[/math]

 

[eddy2017]

24/12=2
Two liters are need to make 12 bags.

 

[Steven G]

Sorry by 24/12 = 2 so 42/12 can't be 2. 2 is not even a close answer in my opinion. Be more careful!

Where does 42/12 come from??

 

[eddy2017]

As I read it, the average is over all the machines, not over many days; so each machine, by itself, produces entire bags, averaging one dozen bags a day.
Each day we make one dozen bags per machine, times 144 machines. How many dozen bags is that?
How much lubricant is needed?.
How many is that per dozen? .

1,728 bags are being manufactured every day.
to find how many dozens there are in 1728 I divide by 12
=144 dozen bags

 

[eddy2017]

How many liters of lubricant are needed to produce a dozen bags?.
How many liters in a day? How many dozen bags in a day? (Dr Peterson #23)
I am stuck here.

 

[Steven G]

As I read it, the average is over all the machines, not over many days; so each machine, by itself, produces entire bags, averaging one dozen bags a day.
Each day we make one dozen bags per machine, times 144 machines. How many dozen bags is that?
How much lubricant is needed?.
How many is that per dozen? .

1,728 bags are being manufactured every day.
to find how many dozens there are in 1728 I divide by 12
=144 dozen bags

You did a lot of work to get that result. If each machine produces one dozen bags and we have 144 machine then it should be immediate that the 144 machines produce 144 dozens of bags. If you don't see that consider if you did the following. You walk by each machine and count-- 1 dozen, 2 dozens, 3 dozen, ... 144 dozens. Does this make sense to you?

 

[eddy2017]

Yes, you're right. It is a simple calculation.

 

[eddy2017]

I feel lost because the original problem has been modified because it makes more sense the way Dr Peterson put it. If you could reword the problem I would appreciate it.

 

[Dr.Peterson]

I feel lost because the original problem has been modified because it makes more sense the way Dr Peterson put it. If you could reword the problem I would appreciate it.

My hope is that my interpretation does not modify the problem, but only clarifies it. Here is the original wording:

In a factory, 144 machines produce an average of a dozen bags in a day. If one liter of lubricant is needed for the gears of 24 machines, how many liters of lubricant are needed to produce a dozen bags?​

Here is how I would have stated it, with minimal change:

In a factory, 144 machines each produce an average of a dozen bags in a day. If one liter of lubricant is needed each day for the gears of 24 machines, how many liters of lubricant are needed to produce a dozen bags?​

I think that's all it takes.

 

[eddy2017]

Great!. So, these are the questions now. I'll try to come up with and answer. If I get stuck, I'll tell you. Thanks.
How many liters of lubricant are needed to produce a dozen bags?.
How many liters in a day?
How many dozen bags in a day?= 144 dozens = 1728 a day. That, at least, is settled.

 

[eddy2017]

Hi, I am working the problem from scratch now that we have the right wording.
144 machine * 12 bags =1,728 bas that are being manufactured on a daily basis. We have already agreed on that).
The following is the question to tackle now.
If one liter of lubricant is needed each day for the gears of 24 machines, how many liters of lubricant are needed to produce a dozen bags?.

This question is asking how many liters of lube is needed for 1 machine. Because the problem says that each machine produces 12 bags (a dozen). Can I validly assume that?.

 

[eddy2017]

If one liter of lubricant is needed each day for the gears of 24 machines, how many liters of lubricant are needed to produce a dozen bags?.
24 machines produce 288 bag, and 1 liter is needed to lube all 24 machines.
to see how many liters of lube are needed to produce a dozen....... stuck here

 

[eddy2017]

I think there might a flaw in the reword of the problem. It is not making any sense for me. The only it would make any sense is if the problem would have been phrased this way.
In a factory, 144 machines each produce an average of a dozen bags in a day. If one liter of lubricant is needed each day for the gears of 24 machines, how many liters of lubricant are needed for each machine to produce a dozen bags? .

 

[Dr.Peterson]

Hi, I am working the problem from scratch now that we have the right wording.
144 machine * 12 bags =1,728 bas that are being manufactured on a daily basis. We have already agreed on that).
The following is the question to tackle now.
If one liter of lubricant is needed each day for the gears of 24 machines, how many liters of lubricant are needed to produce a dozen bags?.

This question is asking how many liters of lube is needed for 1 machine. Because the problem says that each machine produces 12 bags (a dozen). Can I validly assume that?.

If my interpretation is correct (and you really need to ask the source to be sure), then I would agree. It's odd that this means the number of machines (144) isn't really needed; on the other hand, that's how real-life problems work.

So, yes, one way to answer the question is to focus on just one machine.

If one liter of lubricant is needed each day for the gears of 24 machines, how many liters of lubricant are needed to produce a dozen bags?.
24 machines produce 288 bag, and 1 liter is needed to lube all 24 machines.
to see how many liters of lube are needed to produce a dozen....... stuck here

You can do it this way, too. I takes one liter to make 288 bags. How many dozen is that? Then just divide liters by dozens to find liters/dozen.

I think there might a flaw in the reword of the problem. It is not making any sense for me. The only it would make any sense is if the problem would have been phrased this way.
In a factory, 144 machines each produce an average of a dozen bags in a day. If one liter of lubricant is needed each day for the gears of 24 machines, how many liters of lubricant are needed for each machine to produce a dozen bags? .

I don't think that helps, either as a clarification or as a different interpretation of the original. As I'm interpreting it, it just takes one machine to make a dozen bags. This wording sounds like it's talking about all144 machines, which together would make 1728 bags. It's actually more ambiguous rather than less.

But others may have different opinions. This is really about English more than math at this point. Again, you really ask whoever gave you this problem. Where does it come from?

 

[Steven G]

1 liter is for 24 machines. Just divide both sides by 24 to get 1/24 liter is needed for 1 machine.


Think about this similar problem. If you purchased 24 items and the cost is $96. How would you find the price of 1 item?

If you look at post #24 you'll see how to get the answer. All I did was multiply 12 bags by 1 twice and I got that 12 bags = 1/24 liter

 

[eddy2017]

Dr.Peterson
So, yes, one way to answer the question is to focus on just one machine.
You can do it this way, too. I takes one liter to make 288 bags. How many dozen is that? Then just divide liters by dozens to find liters/dozen.

Jomo
1 liter is for 24 machines. Just divide both sides by 24 to get 1/24 liter is needed for 1 machine.

Thank you so much. I see the path clearly now.
And, yes, the problem has been poorly stated. That's a given.
But, thanks, anyway, math is about cudgeling our brains for solutions. It was good practice.

 

[Dr.Peterson]

Dr.Peterson
So, yes, one way to answer the question is to focus on just one machine.
You can do it this way, too. I takes one liter to make 288 bags. How many dozen is that? Then just divide liters by dozens to find liters/dozen.

Jomo
1 liter is for 24 machines. Just divide both sides by 24 to get 1/24 liter is needed for 1 machine.

Thank you so much. I see the path clearly now.
And, yes, the problem has been poorly stated. That's a given.
But, thanks, anyway, math is about cudgeling our brains for solutions. It was good practice.

In the future, please use the Reply button (as I just did) to quote us; merely copying as you did here makes it hard to be sure what is copied.