Final answer:
To find the number of soccer club members going to the tournament, we can set up an equation considering the transportation cost per person. By solving the equation using quadratic formula, we find that there are 7 soccer club members going to the tournament.
Step-by-step explanation:
To solve this problem, we can set up an equation. Let x be the number of soccer club members going to the tournament. The transportation cost per person without the additional students is given by 210/x. When 3 non-club members join, the cost per person decreases by $5.83, so the new transportation cost per person is 210/(x+3).
Since the cost per person without the additional students is $5.83 greater than with the additional students, we can create the equation 210/x = 210/(x+3) + 5.83.
To solve for x, we can cross multiply and simplify the equation. Multiplying both sides by x(x+3) gives us 210(x+3) = 210x + 5.83x(x+3). Expanding, we get 210x + 630 = 210x + 5.83x^2 + 17.49x. Simplifying further, we have 0 = 5.83x^2 + 17.49x - 630.
Using the quadratic formula, x = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = 5.83, b = 17.49, and c = -630, we can solve for x. Plugging in these values, we find x = 7.
Therefore, there are 7 soccer club members going to the tournament.