Word Problem.

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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?
 

Dr.Peterson

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First step: read through the problem (twice, first for an overview, then writing down the data).

Second step: I'd probably sketch a graph, as a way to see the whole story at once.

Third step: Answer each question, by reading through the problem again with that question in mind, while looking at the graph.

You probably have some more specific questions if you've already done any of this! Feel free to show work and ask them.
 

tkhunny

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Model the production.
What sort of shape might the models have?
1) +60 / year
2) -8% / year

Go!

I'm particularly excited to see what you get for #4.
 

Jomo

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1894--100kg for the year

Then increased 60kg each year until it reached 700kg/yr

So how much did it increase if it went from 100kg to 700kg? How many 60kg's is this increase??? If this is too hard then,

100kg + 60kg = 160kg = 1895
160kg + 60kg = 220kg = 1896
220kg + 60kg = 280kg = 1897
...
640kg + 60kg = 700kg =????

You need to figure out some way of doing this problem on your own. Good luck.
 
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@Jomo 1904 I wrote them all out! Note this is sequences and series so I should probably use a formula?
 
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Jomo

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@Jomo 1904 I wrote them all out! Note this is sequences and series so I should probably use a formula?
OK, good. As you become better in Algebra you will see better methods. It takes time to see the best way to do a problem but you need to think of someway of doing this. Good job. Now can you do the rest of the parts?
 

Jomo

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Here is a better way of doing this. You went from 100kg to 700kg which is a 600kg increase. Since you only increased 60kg per year, simply compute 600/60 to get 10 years. Now 1894 + 10 = 1904. Is this clear?
 
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Before I move on. What formula should I have used If I know a=100 d=60 n=?
 
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Question two. First-term is 700kg, I will deduce 8% until I get near/at 300kg
years123456789101112
amount (kgs)700644592.48545.082501.475461.357424.4484390.4925359.253330.513304.072279.746

Production fell below 300kg/year after 12 years? is there a better way to do this with a formula?
 
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