A piggy bank contains $14.55 in quarters, dimes, and nickles. If there was 3 more than twice as many dimes as nickles and three less than three times as many quarters as nickels, how many of each kind of coin was in the piggy bank?

Let

x=number of nickels in the piggy bank

(2x+3) = number of dimes in the piggy bank

(3x-3) = number of quarters in the piggy bank

Now,

.05x+.10 (2x+3) +.25 (3x-3) = 14.55

.05x+.20x+.30+.75x-.75=14.55

1.00x=14.55+.45

x=15

2x+3 = 2 (15) + 3 = 33

3x-3 = 3 (15) - 3 = 42

...

number of nickels in the piggy bank=15

number of dimes in the piggy bank=33

number of quarters in the piggy bank=42

...