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

Answer: (x+2) = 8+2 = 10

Louise has 10 10-cent coins