Let the normal cost for an individual be \( x \). According to the problem, the cost per person with the group package is \( x - 2 \).
Hector's family consists of 5 people, and the total cost with the group package is given as $35. Therefore, we can express the total cost for the family using the formula for the group package cost:
\[ 5 \times (x - 2) = 35 \]
Now, let's solve for \( x \).
- Distributing 5 into the equation gives:
\[ 5x - 10 = 35 \]
- Now, add 10 to both sides to isolate the term with \( x \):
\[ 5x = 45 \]
- Next, divide both sides by 5 to solve for \( x \):
\[ x = 9 \]
Thus, the normal cost for an individual is \( \boxed{9} \).
To verify, we can check the group package cost: If \( x = 9 \), then the cost per person with the group package is \( 9 - 2 = 7 \). The total cost for 5 people would then be:
\[ 5 \times 7 = 35 \]
This matches the information provided in the problem, confirming that the normal cost for an individual is indeed \( \boxed{9} \).