To finance a bridge costing $94,500, the state contributed twice as much as the county and the county contributed twice as much as the city. how much did each contribute?

The city contributed $13,500; the county contributed $27,000; and the state contributed $54,000.

Let x be the amount the city contributes.  Since the county contributes twice as much as the city, the county's amount is 2x.  Since the state contributes twice as much as the county, the state's amount is 2(2x) = 4x.

They total 94,500:
x+2x+4x = 94500
7x = 94500

Divide both sides by 7:
x = 13500
2x = 27000
4x = 54000