1 nickel = 5 cents = $0.05

1 dime = 10 cents = $0.1

let

n = the number of nickels Diane has

d = the number of dimes Diane has

Diane has $1.25 in dimes and nickels

0.05n + 0.1d = 1.25 divide both sides by 0.05

n + 2d = 25

she has a total of 14 coins

n + d = 14

by solving the system of equations

n + 2d = 25

n + d = 14

we find

n = 3 nickles

d = 11 dimes

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Diane has 3 nickles and 11 dimes.