how many days will 2/3 of a bag of cat food feed the......

Ok, it is good that you got the correct answer of 3 days but what is much more important is knowing how you got 3 days.

Can you please explain how you got 3 days and them apply that method to your numbers?
 
2 bags a day * 3 days = 6 bags ( That is how I arrived at 6).
If I followed the same reasoning, could I do the same with the fractions, that is, could I multiply them together?
1/6*2/3
 
eddy2017 said:
2 bags a day * 3 days = 6 bags ( That is how I arrived at 6).
If I followed the same reasoning, could I do the same with the fractions, that is, could I multiply them together?
1/6*2/3
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Well, you can verify that 3 days is the right answer by using multiplication. But that's not how you calculated it. 3 days = ???
 
eddy2017 said:
Oh, it is dividing, not multiplying.
6 days/2bags=3 days
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Yes, it's division. But please be more careful with units: 6 ? /2 ? = 3 days. You have to make sure units on the left and right match.
So, to summarize, given the rate and the total amount of whatever is being consumed, to find time we divide the total amount by rate.
Now, can you use the amounts from the problem?
 
A group of cats consume 1/6 of a bag of food in a day. Each cat eats the same amount of food every day. If the number of cats in the group is halved after adoptions, how many days will 2/3 of a bag of cat food feed the resultant group?.
I am sorry, but I am at a loss as to how we got the 6 and the 2. I did not understand how I got them.
 
eddy2017 said:
A group of cats consume 1/6 of a bag of food in a day. Each cat eats the same amount of food every day. If the number of cats in the group is halved after adoptions, how many days will 2/3 of a bag of cat food feed the resultant group?.
I am sorry, but I am at a loss as to how we got the 6 and the 2. I did not understand how I got them.
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These numbers are not part of the solution of the original problem. I picked them to pose an easier problem, so you could figure out what operation is needed. If you go back you'd see that you wanted to divide the rate by the amount of food. Do you understand that this is wrong? Now that you know what operation is needed you can go back to the original problem and apply this operation.
 
I am going to recap all I have been said and study it and see if i can come up with something. I hope you do not mind my doing so.

the key to such problems is Rate. Calculate (or identify) the rate of consumption, then use it to answer the question. #2

If you have half as many cats, how much will they consume per day?. #4

he question was: "If you have half as many cats, how much will they consume per day?"
Answering it will give you the rate I mentioned. #9

You need to assume that the cats don't just gorge themselves on whatever you give them, but eat what they want. They each eat at a certain rate (in bags per day), and continue to eat at the same rate afterward. #11

If the group of cats consumed 1/6 of a bag of cat feed per day (that is their rate), then the number of cats are reduced by half then what part of a bag will the remaining cats consume per day? #12

Ok, that's the rate.( 1/12) Now, given the rate and the total amount consumed (2/3 of a bag), can you figure out how many days it will last? #15

I said:
Eating at a 1/12 rate out of a 2/3 bag of cat feed.
Division?
1/12÷2/3 ? #16

When you are not sure what operation to use it may help if you replace amounts in the problem by something easier to deal with. E.g. They eat 2 bags a day. How long will 6 bags last? After solving this easy problem just use the same operation with original numbers. #18


Let me reflect on all this helpful hints you have given me. Thank you so much. I'll get back to you. I hope you mind my doing this. It helps me focus when there are several hints and cues and a rather lenghty discussion.
 
It is not that the cats will not gorge on the food as you stated. Eating more than before is very possible! Suppose that the 1/6 of the bag was not enough for the initial set of cats--perhaps they wanted twice as much but it was not offered to them. So when half the cats left the remaining cats could consume the whole 1/6 of a bag. The reason is that you were given that Each cat eats the same amount of food every day. Besides what else can you assume? Maybe the cats only wanted 20% more than what they were initially offered and when their food was doubled they could eat that 20% extra but no more. One can't know this exact amount so we need to assume that each cat will continue to eat the same amount no matter how much food is offered to them.
 
A group of cats consume 1/6 of a bag of food in a day. Each cat eats the same amount of food every day. If the number of cats in the group is halved after adoptions, how many days will 2/3 of a bag of cat food feed the resultant group?.
Thanks, Mr J, for that reflection. Then, if they continue to eat the same amount [1/6] after the other half is taken away, and I am asked how many days 2/3 of a bag will feed the half that stayed, then I think, one way to find that out would be to see how many times 1/6 fits into 2/3.
So,
(1/6)x=2/3 (x for many times)
I need to solve for x, so I multiply both sides times 6
(1/6)x=2/3
6(1/6)x= 6(2/3) [ I think both 6's cancel out]
x= 12/3
x=4

2/3 of a bag of feed will feed them for four days.
Is it correct this way?
Thanks.
 
eddy2017 said:
Then, if they continue to eat the same amount [1/6]
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This is not correct. Each cat continues to eat the same amount - this is different from "the remaining cats will eat the same amount as the original group".
 
Yes, 1/12 is the rate. But I don't know what to do next. Nothing comes to mind. Drop me another hint, please. Don't tell me just give me a hint.
Once I have the rate of consumption, what am I to think about?.

I remember you said this @25

So, to summarize, given the rate and the total amount of whatever is being consumed, to find time we divide the total amount by rate.

Let me think
 
eddy2017 said:
Yes, 1/12 is the rate. But I don't know what to do next. Nothing comes to mind. Drop me another hint, please. Don't tell me just give me a hint.
Once I have the rate of consumption, what am I to think about?.

I remember you said this @25

So, to summarize, given the rate and the total amount of whatever is being consumed, to find time we divide the total amount by rate.

Let me think
Click to expand...
You already solved this with 2 and 6. Just use the same operation with the original amounts.

If you are comfortable with distance/speed/time problems, this is basically the same thing - we are consuming distance at a particular rate, how do we find time?
 
Distance...?
Do I divide the two fractions 1/6 and 2/3 to find the distance?.
 
eddy2017 said:
I have the rate 1/12
t=r*d
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r=d/t is correct. t=r*d is not.
Are you comfortable with distance/speed/time problems?

Anyway, do you understand how to solve this problem with 2 and 6? If you do, what is the difficulty with applying exactly the same operation to the original amounts?
 
t= total amount of cat feed consumed
rate
t= 1/6÷ 1/12. Perhaps?
t=2 days
 
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