Question 169591
i would rather have a kilometer of quarters.
here's why:
in order for me to break even, the diameter of the quarter needs to be 2.5 times the diameter of the dime.
assume the diameter of the quarter is 2.5 and the diameter of the dime is 1.
then 2.5 dimes fit into 1 quarter and i break even.
assume the diameter of the quarter is 3 and the diameter of the dime is 1.
then 3 dimes fit into 1 quarter so i get 30 cents from the dimes and only 25 cents from the quarter.
if the diameter of the quarter is more than 2.5 times the diameter of the dime, then i make more money on the dime.
if the diameter of the quarter is less than 2.5 times the diameter of the dime, then i make more money on the quarter.
the actual diameter of a quarter is 24.26 mm.
the actual diameter of a dime is 17.91 mm.
the ratio is less than 2.5 so the quarter is a better deal since i can only fit 24.26 / 17.91 = 1.35 dimes into a quarter (length only).
this proves out in actual practice.
1 km is equal to 1 million mm
1 million mm / 24.26 = 41220 quarters * .25 = $10,305.
1 million mm / 17.91 = 55835 dimes * .10 = $5,583.
quarters win by a long shot.
the assumption here is that they are lying on their tail side so the thickness of the coin is not a factor.
my choice is a lot better.
$10,305 for the quarters versus $5,583 for the dimes.