1 quarter = 15 cents

1 dime = 10 cents

q = the number of quarters

d = the number of dimes

a collection of quarters and dimes is worth more than $20 = 200 cents:

15q + 10d >= 200 divide both sides by 5

3q + 2d >= 40

there are twice as many quarters as dimes:

q = 2d

plug q = 2d into 3q + 2d >= 40:

3*2d + 2d > 40

by solving we find:

d > 5

click here to see the step by step solution of the inequality:

there are at least 6 dimes.