Question 2 of 10The 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.12B.−12, 10C.10D.−12
Question
Question 2 of 10The soccer club has planned a trip to a tournament. The cost of the van is 3.20. How many soccer club members are going to the tournament?A.12B.−12, 10C.10D.−12
Solution
Let's denote the number of soccer club members as x.
The initial cost per person is $192/x.
When 2 non-members join the trip, the total number of people becomes x+2 and the cost per person drops to $192/(x+2).
According to the problem, the initial cost per person is $3.20 more than the cost per person after the non-members join.
So, we can set up the equation:
192/x = 192/(x+2) + 3.20
To solve this equation, we first multiply all terms by x(x+2) to get rid of the denominators:
192(x+2) = 192x + 3.20x(x+2)
Expanding and simplifying gives:
192x + 384 = 192x + 3.20x^2 + 6.40x
Subtract 192x from both sides:
384 = 3.20x^2 + 6.40x
Divide all terms by 3.20:
120 = x^2 + 2x
Rearrange into a standard quadratic equation:
x^2 + 2x - 120 = 0
Factor the equation:
(x - 10)(x + 12) = 0
Setting each factor equal to zero gives the solutions x = 10 and x = -12.
Since the number of club members can't be negative, the only valid solution is x = 10.
So, there are 10 soccer club members going to the tournament.
The answer is C.10.
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