Sang-jin has only quarters and nickels in her piggy bank. she has 66 coins in the bank with a value of $11.50.

how many quarters are in sang-jin’s piggy bank?

If you had 46 quarters, you would get $11.50, so you know there is less than that because you need 66 total coins. If you had 41 quarters, you would have $10.25. That would mean you need 25 nickles. 41x.25=10.25  25x.05=1.25  10.25+1.25=11.50. So your answer would be 41 quarters are in the bank.

AG. 
Sorry, this took so long... hehe but, I got your answer, through lots of trial and error. Thanks for being patient with me :)

So, I can't explain it in numbers, because you would be reading this for another 10 minutes, becoming more and more confused. In the end, I got 41 quarters, and 25 nickels. I REALLY hope this helps. Lemme know if you need another one done. :)