When a child breaks open her piggy bank, she finds a total of 76 coins, consisting of nickels, dimes, and quarters. The total value of the coins is $9. If the nickels were dimes, and the dimes were nickels, the value of the coins would be $8. How many nickels, dimes, and quarters were in the piggy bank?

Answer 1

nickels --- n
dimes ---- d
quarters --- (76-n-d)

5n + 10d + 25(76-n-d) = 900
5n + 10d + 1900 - 25n - 25d = 900
-20n - 15d = -1000
4n + 3d = 200 , #1

if nickels = d
dimes = n
quarters is still 76-n-d

5d + 10n + 25(76-n-d) = 800
5d + 10n + 1900 - 25n - 25d = 800
-15n - 20d = -1100
3n + 4d = 220 , #2

#1 times 4 : 16n + 12d = 800
#2 times 3: 9n + 12d = 660
subtract them
7n = 140
n = 20
back in #1:
80+3d=200
3d=120
d=40
then quarters = 76-20-40 = 16

there were 20 nickels, 40 dimes and 16 quarters in the bank