Add 6 dimes to the collection (mentally). Then the collection will have equal number of dimes and quarters and be worth 465 + 6*10 = 525 cents. Hence, you can group all coins in this new collection in pairs, 1 dime + 1 quarters in each pair. Each pair is worth 25+10 = 35 cents, and the number of these pairs is 525/35 = 15. Hence, the original collection had 15 quarters and 15-6 = 9 dimes. ANSWER