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, w² coins from bag #3, w³ coins from bag #4, and w⁴ 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.