Word Problem.

JeffM said:
This is a terrible question because the problem (at least as stated) gives no clue about how much was there to begin with.

So, as tkhunny hinted in post #2, the question (at least as stated) is technically unanswerable.

Thus, the first thing to do is to go back to the statement of the problem and see if you missed something.

If not, you will have to guess what the question means. My guess is that it is asking you to assume that, approximately, everything that is there is in the process of being extracted. So the total there originally is equal to what was extracted before mining ceased and what could be extracted if mining continued until the amount left was approximately zero. (You cannot get to zero by 8% reductions, but a balance below 10 would give a total accurate to considerably better than 1% given that total extraction is already in the thousands.)
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I went back and had a look what I posted is all the information given. This is confusing!
 
JeffM said:
This is a terrible question because the problem (at least as stated) gives no clue about how much was there to begin with.

So, as tkhunny hinted in post #2, the question (at least as stated) is technically unanswerable.

Thus, the first thing to do is to go back to the statement of the problem and see if you missed something.

If not, you will have to guess what the question means. My guess is that it is asking you to assume that, approximately, everything that is there is in the process of being extracted. So the total there originally is equal to what was extracted before mining ceased and what could be extracted if mining continued until the amount left was approximately zero. (You cannot get to zero by 8% reductions, but a balance below 10 would give a total accurate to considerably better than 1% given that total extraction is already in the thousands.)
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what do you mean by a balance below 10? do you mean when the extraction of gold is less than 10kg/yr? if so that's roughly the 47th year? and are you saying that there would only be 1% of the gold left in the mine? wouldn't you keep deducting 8% from the 11th year until you reach close to zero add all the values of extraction that could have been in the mine if it was still open to get a percentage?
 
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amathproblemthatneedsolve said:
what do you mean by a balance below 10? do you mean when the extraction of gold is less than 10kg/yr? if so that's roughly the 47th year? and are you saying that there would only be 1% of the gold left in the mine? wouldn't you keep deducting 8% from the 11th year until you reach close to zero add all the values of extraction that could have been in the mine if it was still open to get a percentage?
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I am saying that one guess as to what is intended by the problem is to assume that if extraction continued to follow the same course, it would take infinite time to exhaust the silver available completely.

You have already extracted thousands of kg. If you track how much will be extracted until you are extracting at most 5 or 10 kg per year, the relative amount remaining to be extracted will be small compared to what has been extracted so estimating the original amount by what was already extracted will be an under-estimate, but not a gross under-estimate.
 
JeffM said:
I am saying that one guess as to what is intended by the problem is to assume that if extraction continued to follow the same course, it would eventually exhaust the silver available.
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Yes, I agree with this 'guess'.

JeffM said:
You have already extracted thousands of kg. If you track how much will be extracted until you are extracting at most 5 or 10 kg per year, the relative amount remaining to be extracted will be small compared to what has been extracted so estimating the original amount by what was already extracted will be an under-estimate, but not a gross under-estimate.
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What I was saying was couldn't you figure out how much silver in percentage was left in the ground by reducing the amount you get each year by 8% as I was doing before, but instead, you tally up the amount of silver that would have been extracted if the mine was still open and then convert that to a percentage and that would be the amount of silver remaining in the ground after the mine ceased operation? I guess were saying similar things.
 
amathproblemthatneedsolve said:
Yes, I agree with this 'guess'.


What I was saying was couldn't you figure out how much silver in percentage was left in the ground by reducing the amount you get each year by 8% as I was doing before, but instead, you tally up the amount of silver that would have been extracted if the mine was still open and then convert that to a percentage and that would be the amount of silver remaining in the ground after the mine ceased operation? I guess were saying similar things.
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Yes. That is what I am saying. Of course the sum of the annual extractions will never exactly equal what was originally there because some is always left, but, unless you know infinite series, that is the best you can do.
 
Subhotosh Khan said:
What did you need to "find"?
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The question says to 'Calculate the percentage of silver remaining in the ground after all mining operations ceased' so I know two things a( the answer is a percentage and b( I need to find the silver remaining in the ground after mining has stopped
 
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amathproblemthatneedsolve said:
Sum of the infinite series is 8750 so do I convert this to a percentage now ?
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If I do initial amount mined ( mine A's and mine B's total extraction over there operating years ), then that would be 3,533+11,400=14933 so then doing

8750 (amount mined after the operation was closed) 8750/14933 =0.585951

0.585951x100= 58.5951% and (1-0.585951)x100=41.4049%

is this right? and if so what do my results mean? was 58.5951% of the gold mined and 41.4049% gold left ?
 
amathproblemthatneedsolve said:
If I do initial amount mined ( mine A's and mine B's total extraction over there operating years ), then that would be 3,533+11,400=14933 so then doing

8750 (amount mined after the operation was closed) 8750/14933 =0.585951

0.585951x100= 58.5951% and (1-0.585951)x100=41.4049%

is this right? and if so what do my results mean? was 58.5951% of the gold mined and 41.4049% gold left ?
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Where did you calculate those two numbers 3,533 & 11,400? (please indicate the post # - it is given in the top right corner. The post # of this post is #32)
 
@Subhotosh Khan

I don't think I did calculate them on here, but how I got them is summing both sequences individually, note once the first mine reaches 700kg/yr it keeps producing that amount util 1914 so in the formula I used [MATH]S₁₁ = 11/2 \times(2\times100(11+1)\times60) S₁₁=4400 [/MATH] then add [MATH] 700\times10 =11,400[/MATH] How I got 3,533 I just summed up it until it closed as normal (using the geometric formula though).

@JeffM is my post #31 right? or close
 
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amathproblemthatneedsolve said:
@Subhotosh Khan

I don't think I did calculate them on here, but how I got them is summing both sequences individually, note once the first mine reaches 700kg/yr it keeps producing that amount util 1914 so in the formula I used [MATH]S₁₁ = [COLOR=rgb(243, 121, 52)][B]11/2 \times(2\times100(11+1)\times60)[/B][/COLOR] S₁₁=4400 [/MATH] then add [MATH] 700\times10 =11,400[/MATH] How I got 3,533 I just summed up it until it closed as normal (using the geometric formula though).

@JeffM is my post #31 right? or close
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Are you saying you got:

S11 = 11/2 * 2 * 11 * 100 * 12 = 4400

That is not correct! (However you wrote the value of the sum correctly)

Sn = n/2 * [2*a + (n-1)*d] = 11/2 * [2*100 + 10 * 60] = 4400

What geometric formula did you apply?
 
Subhotosh Khan said:
Are you saying you got:

S11 = 11/2 * 2 * 11 * 100 * 12 = 4400

That is not correct! (However you wrote the value of the sum correctly)

Sn = n/2 * [2*a + (n-1)*d] = 11/2 * [2*100 + 10 * 60] = 4400

What geometric formula did you apply?
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Firstly, yes that was a mistake sorry. and Secondly, I did [MATH]S₁₂=700 \times 1- (23/25)¹²[/MATH] that's over 1- (23/25)

I don't know how to write it with LaTeX but the formula is here [MATH]\Longrightarrow[/MATH]
Screenshot 2019-09-25 at 8.54.30 AM.png
 
amathproblemthatneedsolve said:
A Mining Company was founded in 1894 and the mine’s initial production was the extraction of 100kg/year of silver. Each following year saw a steady increase of 60kg/year until the silver production peaked at 700 kg/year. Production remained at this level until 1914, when an event caused the mine to close indefinitely. The company then stopped its mining operations on the claim during the First World War (1914–1918). In 1920, the company opened up a new second mine which, in the first year, saw a silver yield of 700kg/year. However, with every subsequent year, production decreased by 8%. For economic reasons, the new mine had to close when the production fell below 300kg/year.

1. When did the first mine reach the peak production of 700 kg/year?

2. How long was the second mine operating for?

3. Compare the production of both mines over the first five years. Find the total production figures of the two mines until that ceased operation. which of the two mines was more successful? Provide evidence and explain the reasons behind your decision.

4. Calculate the percentage of gold remaining in the ground after all mining operations ceased.

first steps?
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Like several tutors pointed out - this problem is flawed!

1) How can you calculate % of gold remaining in a silver mine? The silly answer would be 0%.

2) How much metal was left in the first mine? We cannot calculate that from given information. Do they want you calculate (the percentage of metal remaining in the ground) for the 2nd mine only?
 
Subhotosh Khan said:
Like several tutors pointed out - this problem is flawed!

1) How can you calculate % of gold remaining in a silver mine? The silly answer would be 0%.

2) How much metal was left in the first mine? We cannot calculate that from given information. Do they want you calculate (the percentage of metal remaining in the ground) for the 2nd mine only?
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1) that was my typo.

and 2) yes they do I guess.
 
Subhotosh Khan said:
In that case, recalculate:

Total metal available in mine #2

Then divide the the total amount un-extracted (from mine #2) by the number above and express it as %.
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Isn't total metal in mine #2 just 3,533 so divide that by 8750 = 0.40377142857 x by 100 = 40.377142857%? that's the amount left in the mine?
 
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