1 dime = 10 cents

1 quarter = 25 cents

let

d = the number of dimes

q = the number of quarters

Two thirds of the coins in a collection of quarters and dimes are quarters

(2/3)(q + d) = q

The collection is worth $12 = 120 cents

10d + 25q = 120 divide both sides by 5

2d + 5q = 24

by solving the system of equations

(2/3)(q + d) = q

2d + 5q = 24

we find

d = 2 dimes

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

there are 2 dimes in the collection.