Math Project Help Again...?

Question

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? Show work...

Answer 1

Hi,

When the amount doubles each square, this is looking for the sum of a geometric series where the first term, a, is 1 and the common ratio, r, is 2. The formula for this sum is:

S = a(1-r^n)/(1-r)

For 32 squares, this would be

S = 1(1-2r^32)/(1-2) = $42,949,672.95


I hope that helps!

Answer 2

make a chart starting at 1 and doubling it every line for 32 lines and you will get your answer.. AND you will have shown your work.