Let represent the number of dimes. Then Let must be the number of nickels. Each of his dimes is worth 10 cents, so the value of his dimes is Let cents. Each nickel is worth 5 cents, so the value of the nickels is cents. Total value of his money is $1.65, which is to say 165 cents. Since he presumably has no coins other than the dimes and the nickels:
Solve for to get the number of dimes, then add 12 to that to get the number of nickels. Check by adding up the amount of money that many coins represents -- it should work out to $1.65.