a) the weight of any coin (in ounces) is a positive integer less than or equal to w

b) all coins in a given bag weigh the same

c) the weight of a coin in bag #1 is different from the weight of a coin in bag #2

d) when one coin from bag #1, w coins from bag #2, w^{2} coins from bag #3, w^{3} coins from bag #4, and w^{4} coins from bag #5 are combined and weighed, the result is 2800 ounces

Determine analytically, the weight of a coin in each of the five bags.