1 nickle = 5 cents

1 dime = 10 cents

let

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

d = the number of dimes, d>0, d is integer

Dave has 60 coins, all dimes and nickels

d + n = 60

they are worth $4.80 = 480 cents

10d + 5n = 480 divide both sides by 5

2d + n = 96

by solving the system of equations

d + n = 60

2d + n = 96

we find

d = 36 dimes

n = 24 nickles

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Dave has 36 dimes and 24 nickles.