Question

The soccer club has planned a trip to a tournament. the cost of the van is $192. when 2 students who are not members of the club join the trip, the transportation cost per person drops by $3.20. how many soccer club members are going to the tournament?

a. -12
b. 10
c. -12,10
d. 12

Answer 1

To find the number of soccer club members going to the tournament, we set up an equation based on the change in transportation cost per person. After solving the equation, we conclude that there are 10 soccer club members attending the tournament.

Step-by-step explanation:

The student is asking to find the number of soccer club members going to the tournament based on a change in transportation cost per person when additional students join the trip.

Let the number of original club members be x. The transportation cost per person for the original number of members is $192/x. When two non-members join the trip, the new cost per person becomes $192/(x + 2), which we know is $3.20 less than the original cost per person. This gives us the equation:

192/x - 192/(x + 2) = 3.20

To solve for x, we will find a common denominator and simplify the equation:

1. Multiply both sides by x(x + 2) to clear the denominators.
2. Simplify and solve the resulting quadratic equation.
3. Discard the negative solution since it doesn't make sense in this context.

The solution to the equation is x = 10, meaning 10 soccer club members are going to the tournament.