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Which Wages?
 
Q A man applied for a job. The woman who interviewed him offered him two pay rates: a straight rate of $100 a day or a pay rate that would begin at one cent the first day and then double each day. The second rate meant the man would earn two cents the second day, four cents the third day, eight cents the fourth day, and so on. The man chose the second rate, and the woman hired him.

Tell why, and prove your case.


 
A The woman hired the man because she wanted a smart employee, and he was smart enough to figure out that he would accumulate much more money at the second pay rate as soon as he got to the 18th day of work. It's true that at Day 10, the first rate would pay him a total of $1,000, for the first 10 days and the second rate would pay him a total of only $10.23 for the same ten days. By day 19, however, the first rate would earn him a total of $1,900, but the second rate would earn him $2,621.44 just for that day! And the man's earnings would keep increasing by leaps and bounds.

Source:The Best of Brain Teasers from Teacher Created Materials,p. 127