Hector and his family are heading to Tiny Acres Mini-Golf. They plan to purchase the group package. With the group package, the cost per person is $2 less than the normal cost for an individual. There are 5 people in Hector's family. His mom called ahead and found that the total cost for the family will be $35. What is the normal cost for an individual?

Question

GPT-4o mini · Answer

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} $.