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Question 44597: A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
Show work in this space
c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?
Answer:
Show work in this space
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
$21474836.48
Show work in this space
an = .01*2n-1
a32 = .01*232-1
a32 = .01*231
a32 = .01 * 2147483648
a32 = 21474836.48
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
$42949673.00
Show work in this space
Sum an = .01 * (2n - 1) / ( 2 - 1 )
Sum a32 = .01 * (232 - 1) / ( 2 - 1 )
Sum a32 = 42949673.00
c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?
Answer:
$184467000000000000.00
Show work in this space
Sum an = .01 * (2n - 1) / ( 2 - 1 )
Sum a64 = .01 * (264 - 1) / ( 2 - 1 )
Sum a64 = 184467000000000000.00
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