Let's use the variable 'x' to represent the number of 30c cards and the variable 'y' to represent the number of 35c cards.
If the total price of the box is $5.80, we can write the equation:

If the number of 30c cards is six more than half the number of 35c cards, we have that:

Using this value of x in the first equation, we have:

So the number of 35 cards is 8.