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

Brianna has fourteen fewer pennies than nickels:

p = n - 14

Brianna has a total of $1.72 = 172 cents:

p + 5n = 172

By solving the system of equations:

p = n - 14

p + 5n = 172

........

........

p = 17 pennies

n = 31 nickles

Brianna has 17 pennies and 31 nickels.