Call the original number of $10 notes, M
Call the original number of $2 notes , N
So
10M + 2N = 2280 (1)
If 4 pieces of $10 notes were exchanged for $2 notes of the same value....then the number of $2 notes must increase by 20 since after the exchange and the number of $10 notes must decreases by 4....and since we have the same number after the exchanges.....then
So
M - 4 = N + 20
M = N + 24 (2)
Sub (2) into (1) and we have that
10 (N + 24) + 2N = 2280 simplify
10N + 240 + 2N = 2280 subtract 240 from both sides
12N = 2040 divide both sides by 12
N = 170 = number of $2 notes originally
Proof
There were 170 $2 notes originally and
10M + 2 (170) = 2280
10M + 340 = 2280
10m = 2280 - 340 =
10M = 1940
M = 194 $10 notes originally
After the exchange there are 170 + 20 = 190 $2 notes and 194 - 4 = 190 $10 notes