if I have 1.60g of urea, how much water, in grams, should be added in the preparation of a 23.1 percent by mass solution?

You want 23.1% w/w which means 23.1 g urea in 100 grams solution.

(1.6/x)*100 = 23.1
Solve for x for TOTAL mass.
I obtained about 7 g total (only approximate--you need to do it more accurately)--so you want about 7-1.6 = ? g H2O