SOLUTION: The other one didnt help 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 f

Question 74135: The other one didnt help

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.
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
Found 2 solutions by stanbon, funmath:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space
The 1st square has 2^0=1 penney
The 2nd square has 2^1=2 pennies
The 32nd square has 2^31 pennies
2^31= $21,474,836.48
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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
1+2+4+8+...+2^31
This is a geometric series.
The sum of n terms is S(n)=a[r^(n+1)-1]/[r-1]
S(32) = 1[2^33 -1]/[2-1]=2^33-1= $85,899,345.91
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c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?
Answer:
Show work in this space
S(64) = 1[2^65 - 1]/[2-1] = 2^65 -1 =$(3.689438815 x 10^19)
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Cheers,
Stan H.

Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
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.
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:$21,474,836.48
Show work in this space
This is a geometric series:
1,2,4,...
2^0,2^1,2^2
a=1 and r=2

This is in cents, so put a dollar sign in front and a decimal two spots from the end.

:
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:$42,949,672.95
Show work in this space

n=32, r=2

Again, express this in dollars.

:
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: $184,467,440,737,095,516.15
Show work in this space
Use the same formula from b, n=64 and r=2

Again express the money in dollars.
Double Check everything, it's real easy to get numbers out of order or something when there's that many of them.
Happy Calculating!!!!
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