1 dime = 10 cents

1 quarter = 25 cents

let

d = the number of dimes

q = the number of quarters

there are 37 dimes and quarters in all

d + q = 37

the combined value of the dimes and quarters is $ 4.60 = 460 cents

10d + 25q = 460 divide both sides by 5

2d + 5q = 92

by solving the system of equations

d + q = 37

2d + 5q = 92

we find

d = 31 dimes

q = 6 quarters

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there are 31 dime.