Wei Xiang has been saving part of his allowance in a bag every month. The bag containing $2 and $10 notes had a total value of $1284. 8 pieces of $10 notes were exchanged for $2 notes of the same value. In the end, the number of $10 notes was the same as the $2 notes. How many $2 notes were there at first?
+33659 Let t be initial number of $2 notes and n be initial number of $10 notes.
2t + 10n = 1284 (1)
8 pieces of $10 notes are equivalent to 40 pieces of $2 notes, so:
t+40 = n - 8 (2)
Rearramge (2) to get: n = t + 48. Put this into (1):
2t +10(t + 48) = 1284
12t + 480 = 1284
12t = 804
t = 804/12 or t = 67
So there were 67 $2 notes initially.
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