1 quarter = 25 cents

1 dime = 10 cents

Let

q = the number of quarters, q>=0, q is integer

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

Connor has $9.00 = 900 cents in dimes and quarters:

10d + 25q = 900

he has twice as many quarters as dimes:

q = 2d

We have the following system of equations:

10d + 25q = 900

q = 2d

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d = 15 dimes

q = 30 quarters

Connor has 15 dimes and 30 quarters.