A clever girl figured out a great way to catch fish in the Underwater Fishing Cavern. The first day she went fishing, she caught exactly 31416 pounds of fish!
Even though she had more fish than she knew what to do with, she decided to go fishing again the next day. And she caught exactly 40% of what she caught the day before. Which was still a lot of fish.
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.
2007-05-24 06:27:10 · 3 answers · asked by julz_rulz_all 2 in Science & Mathematics ➔ Mathematics
Every year has let's say 365 days. 20 years is 7300 days.
Total amount of fish during 20 years is =
31416( 1 + 0.4 + 0.4^2 + 0.4^3+.......0.4^7299).
Inside the parentheses you have a geometric series
In general the sum S of a geometric series with a ratio r, the firs term q , and n terms is:
S = q* [ (1-r^n)/(1-r)]
In our case:
q = 1
r = 0.4
and n = 7300
So S = (1 - 0.4^7300)/ ( 1 - 0.4) = 1/0.6 = 1.7
Total amount of fish is 31416*1.7 = 53407 pounds
2007-05-24 06:51:24 · answer #1 · answered by ali j 2 · 0⤊ 1⤋
OK so you know that the first day she caught 31,416 pounds of fish.And when she went fishing the next day she caught 40% of what she caught the day before. So first you need to figure out how much she caught the next day. I think it is easier to find that number when you cross multiply and divide. So you would put 40 over 100 and nothing over 31,416. And all you have to do know is say 40 times 31,416 which equals 1,256,640.Then you divide that number into 100 which equals 12,566. And that is how many pounds she caught the next day. Then you want to know if she continues to fish every day for 20 years how many pounds in all would she catch. So to find that out you first need to find out how many days are in 20 years. There are 365 days in a year so just times that by 20 which equals 7,300 days. Then you cross multiply and divide 7,300 over 100 and nothing over 12,566 and you get your answer 917,318.
So I THINK the answer is 917,318
I hope it is right i tried my best. :) Sorry if i got it wrong.
2007-05-24 06:50:43 · answer #2 · answered by Anonymous · 0⤊ 1⤋
31416 + (.4)(31416) + (.4)²(31416) + .... =
31416[ 1 + .4 + .4² + ... + .4^7304 ] =(includes 5 leap year days)
31416[ 1 - .4^7305] / [1 - .4] =
52,360
2007-05-24 06:46:37 · answer #3 · answered by Philo 7 · 1⤊ 0⤋