Louise has only 5 cent, 10 cent, and 20 cent coins in her purse. she has 30 coins in total, and she has two more 10 cent coins than 5 cent coins. if the total value of her coins is $3: 80, how many 10 cent coins does she have?

Let x =  number of 5 cent coins.
Then there are (x+2) 10 cent coins.
Let y = 20 cent coins.
Total coins: x+(x+2)+y = 30
2x+y=28       
y = 28-2x                             (1)
Total value: 0.05x + 0.1(x+2) + 0.2y = 3.80
0.15x + 0.2y + 0.2 = 3.80
0.15x + 0.2y = 3.60             (2)
Substitute (1) into (2).
0.15x + 0.2(28-2x) = 3.60
-0.25x + 5.60 = 3.60
2.00 = 0.25x
8 = x

From (1), obtain y = 28 - 2(8) = 12
(x+2) = 8+2 = 10 
Louise has 10 10-cent coins