Question 135052
Let d be the number of dimes.
Let n be the number of nickels.

Given:
total number of coins = 218 = number of dimes + number of nickels => 
{{{218 = d+n}}}

total value of coins = 16.05 = 0.10d + 0.05n  (multiply the value of each coin by   the number and then add the totla for both types of coins) --> 
{{{1605 = 10d + 5n}}}   lets convert from dollars to pennies to make things easier (we just multiplied the eqaution above by 10)

You now have 2 equations and 2 unknowns, so you can solve this.
{{{218 = d+n}}}
{{{218 - n = d}}}
{{{1605 =10d + 5n}}}
{{{1605 = 10(218 - n) + 5n}}} 
{{{1605 = 2180 - 10n + 5n}}}
{{{-575 = -5n}}}
{{{115 = n}}}
You have 115 nickles.
218-115 = 103 dimes

Check your answer 
10.30 in dimes + 5.75 in nickels = $16.05. check!