1 penny = 1 cent

1 nickle = 5 cents

let

p = the number of pennies

n = the number of nickles

Patty has a total of $1.60 = 160 cents of pennies and nickels

p + 5n = 160

there are 10 more pennies than nickels

p = 10 + n

by solving the system of equations

p + 5n = 160

p = 10 + n

we find

p = 35 pennies

n = 25 nickles

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Patty has 35 pennies and 25 nickles.