let

n = the number of nickles, n is positive integer

d = the number of dimes, d is positive integer

1 nickle = 5 cents = $0.05

1 dime = 10 cents = $0.1

Susan paid for her library fine with 26 coins consisting of nickels and dimes

n + d = 26

the fine was $2.10

0.05n + 0.1d = 2.10

by solving the system of equations

n + d = 26

0.05n + 0.1d = 2.10

we find

n = 10 nickles

d = 16 dimes

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Susan had 10 nickles.