SOLUTION: Can you tell me if my answers are correct? CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed a

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Can you tell me if my answers are correct? CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed a      Log On

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Question 84069: Can you tell me if my answers are correct?
CLASSIC PROBLEM - 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.
How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer: $21474836.48
Show work in this space

2 ^ (32 – 1) = 2147483648 pennies = $21474836.48

How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer: $42949672.95
Show work in this space
1 * (1 – 2 ^ 32) / (1 – 2) = 4294967295 pennies = $42949672.95

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: $184467440737095516.16
Show work in this space
1 * (1 – 2 ^ 64) / (1 – 2) = $184467440737095516.16

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Your first answer is correct:
The number of pennies on the 32nd square would be:
2%5E%2832-1%29+=+2%5E31 = 2147483648 and this would be: $21,474,836.48 which is exactly what you have!
Your second answer is correct.
The total amount on a 32-square checkerboard would come to:
2%5E32+-+1+=+4294967295pennies and this would be: $42,949,672.95
Your third answer seems to be off by a penny:
The total amount on a 64-square checkerboard would be:
2%5E64+-+1+=+18446744073709551616-1pennies and this would be: $184,467,440,737,095,516.15