1 dime = 10 cents

1 quarter = 25 cents

let

d = the number of dimes

q = the number of quarters

You have a piggy bank containing a total of 61 coins in dimes and quarters

d + q = 61

the piggy bank contains $10.30 = 1030 cents

10d + 25q = 1030 divide both sides by 5

2d + 5q = 206

by solving the system of equations

d + q = 61

2d + 5q = 206

we find

d = 33 dimes

click here to see the step by step solution of the system of equations

there are 33 dimes in the piggy bank.