A Billionaire offers to give you (1) $1.9 billion if you will first count the amount in $1 bills or (2) a lump sum of $5000. (Assume that you can count at an average rate of one bill per second, and be sure to allow for the fact that you will need about 10 hours a day for sleeping and eating. Your answer does not need to be limited to one significant figure.)
(a) How long would it take you to count the amount in $1 bills?
years(b) Which offer should you accept?
(a) How long would it take you to count the amount in $1 bills?
years(b) Which offer should you accept?
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If you count $1 per second and can only utilize 14 hours a day (due to the 10 taken for sleeping and eating that they mention), simply find how many seconds are in a day first.
14 hours * 60 minutes per hour * 60 seconds per minute = 50400 seconds you have to count per day.
Which also means you count $50400 each day.
Now, divide the total of 1900000000 by 50400 to see how many days it will take you to count all the money.
1900000000/50400 = 37698.4127 days to count to 1.9 billion
We can go further and find the years by dividing by 365 and get 103.283 years.
(It mentions significant figures in the first problem to say that you do not need to limit your answer based on significant figures, so this isn't a significant figure problem actually).
b) Take the $5000, you'll die before you count the $1.9 billion. And even if you allowed yourself more time each day to actually spend the money you count, it says you have to count it all first and then you get the money.
14 hours * 60 minutes per hour * 60 seconds per minute = 50400 seconds you have to count per day.
Which also means you count $50400 each day.
Now, divide the total of 1900000000 by 50400 to see how many days it will take you to count all the money.
1900000000/50400 = 37698.4127 days to count to 1.9 billion
We can go further and find the years by dividing by 365 and get 103.283 years.
(It mentions significant figures in the first problem to say that you do not need to limit your answer based on significant figures, so this isn't a significant figure problem actually).
b) Take the $5000, you'll die before you count the $1.9 billion. And even if you allowed yourself more time each day to actually spend the money you count, it says you have to count it all first and then you get the money.