Total number of stamps = 88 stamps.
Let us assume number of 25 cent stamps = x.
Number of 2 cents stamps = y.
x+y = 88 -------------------(1).
Total cost of 25 cent x stamps = 0.25 x.
Total cost of 2 cents y stamps = 0.02y.
Total value of all stamps = $15.56.
Therefore,
0.25x + 0.02 y = 15.56 -------------------(2).
Solving first equation for y, we get
y = 88 -x.
Substituting y=88-x in second equation, we get
0.25x + 0.02 (88 -x) = 15.56
0.25x + 1.76 - 0.02x = 15.56
0.23x +1.76 = 15.56
0.23x = 15.56-1.76
0.23x = 13.80.
Dividing both sides by 0.23, we get
x = 60.
Plugging x=60 in first equation
60+y = 88
y = 88-60
y = 28.
Therefore, number of 25 cents stamps 60 and number of 2 cents stamps 28.