In primary school, we learnt how to do using guess and check:
In secondary school, we will make use of algebra to create statements and solve the variables accordingly:

Let x be number of $0.20 coins,
Y be number of $0.50 coins:
We craft the 2 statements,
1 in number of coins, 1 in the value of coins:
X + Y = 54 ---(1)
0.2X + 0.5Y = 20.70 ---(2)
Now solve simultaneously:
(1): X = 54 - Y ---(3)
Sub (3) into (2):
0.2 (54 - Y) + 0.5Y = 20.70
10.80 - 0.2Y + 0.5Y = 20.70
0.3Y = 9.90
Y = 33
:. Sub into (3): X = 21

:. There are 21 $0.20 and 33 $0.50