Ahotel manager found that his gross receipts for the day, including a 3 % sales tax, were $3554.53. find the amount of sales tax collected

The gross receipts would include the sales profit and the sales tax. We let sales profit be the variable x. The equation we can make from the word problem would be

Gross profit = x + 0.03x = $3554.53

The sales tax is taken as the percentage of the total sales profit. Solving for x,

1.03x = 3554.53
x = 3554.53/1.03
x = $3451

The sales tax is equal to
Sales tax = 0.03($3451) = $103.53

False because how does that work?