A jeweler has five rings, each weighing 18 grams, made of an alloy of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 45 %. How much silver should he add?

five rings, 18 grams each, so the total is 18*5=90 grams
suppose he adds x grams of silver, the total weight will be 90+x grams
out of these 90+x grams, 45% of it is gold, so the amount of gold is 0.45(90+x)
this amount of gold is the same as the old amount, which is 90% of 90=81, because no gold was added.
so we have an equation: 0.45(90+x)=81
solve: 90+x=81÷0.45=180
x=90
He needs to add 90 grams of silver.