In 20 years, how many pounds of fish would she catch?

[justagirlneedinyourhelp]

Sarah figured out a great way to catch fish. The first day she went fishing, she caught exactly 31416 pounds of fish! She decided to go fishing again the next day and she caught exactly 40% of what she caught the day before. She continued fishing every day. And every day she caught exactly 40% of what she caught the previous day. If she continued fishing every day for twenty years, how many pounds of fish, total, would she catch? Please round to the nearest pound.

I really have no idea! Please please help, i dont even know where to start!

 

[stapel]

You posted this to "Arithmetic", which suggests that you haven't yet taken pre-algebra, let alone algebra. Have you done anything with percentages yet?

By the way, you might want to have your parents complain about your elementary-school teacher assigning you the latest Neopets "Lenny Conundrum" contest question for homework, especially when, as a grammar-school arithmetic student, you don't have the tools to win prizes for her. :? :evil:

Eliz.

 

[TchrWill]

Sarah figured out a great way to catch fish. The first day she went fishing, she caught exactly 31416 pounds of fish! She decided to go fishing again the next day and she caught exactly 40% of what she caught the day before. She continued fishing every day. And every day she caught exactly 40% of what she caught the previous day. If she continued fishing every day for twenty years, how many pounds of fish, total, would she catch? Please round to the nearest pound.

As stapel pointed out, having posted your problem in the arithmetic area might indicate that you have not yet been exposed to the method for solving a problem of this type. On the other hand, if you just posted the problem there for some unknown reason and have some exposure to solution methods,, the problem itself is somewhat far fetched in that no fish would be caught after 20 years, if years is really what you meant.

The first days catch of 31,416 lbs. of fish is reduced by 60% each subsequent period of time. The sequence of caught quantities would look like the following:
Time....1......2.....3....4...5...6...7..8...9.10.11.12
Lbs..31,416.12,566.5026.2010.804.321.128.51.20.8..3..1
(Quantities have been rounded off to the nearest integer as a fraction of a fish does not count)

You talk in terms of catchig the quantities shown each day as opposed to the total time period of 20 years that you state. As you can readily see, she would catch no more fish after the 12th day, week,, month or year making the period of 20 years meaningless to the problem. If you stated the question in terms of yearly catches, no more fish would be caught after the 12th year, never reaching 20 years.

Just in case you have some knowledge of what a geometric series is, the numbers of pound caught form a geometric series where each successive term is multiplied by a constant factor. Your series has fhe first term of 31,416, last term of 1, common factor of 0.40 and number of terms of 12. The sum of a geometric series is given by S = a(r^n - 1)/(r - 1) where a = the first term, r = the common factor and n = the number of terms.
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Edited by stapel -- Reason for edit: Respecting Neopets' contest policy of not posting solutions until after contests close.

 

[stapel]

With the explanation and formula provided in the preceding reply, you can compute the solution for yourself, if you have sufficient background. If not, please wait until after the contest closes (probably 30 May 2007), and reply with your request.

Thank you!

Eliz.