1 penny = 1 cent

1 nickle = 5 cents

let

p = the number of pennies, p>0, p is integer

n = the number of nickels, n>0, n is integer

john has $9.60 = 960 cents in pennies and nickels:

1*p + 5*n = 960

there are thrice as many nickels as pennies:

n = 3p

by solving the system of equations:

1*p + 5*n = 960

n = 3p

we find:

p = 60 pennies

n = 180 nickels

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John has 60 pennies and 180 nickles.