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 , thw transportation cost per person drops by $3.20. how mant soccer club members are gpoing to the tournament

Answer 1

192 divided by 3.20 is 60
60 - 2 is 58 
So, 58 soccer club members are going to the tournament.

Answer 2

Answer:

10 soccer club members are going to the tournament.

Step-by-step explanation:

Let x be the number of soccer club members who are going to the  tournament,

Given,

The cost of transportation of x students = $ 192

⇒ The cost of transportation of 1 student = $\frac{192}{x}$

⇒ The cost of transportation of (x+2) student = $\frac{192}{x-2}$

According to the question,

$\frac{192}{x}-\frac{192}{x+2}=3.20$

$192(\frac{1}{x}-\frac{1}{x+2})=3.20$

$192(\frac{x+2-x}{x(x+2)})=3.20$

$\frac{384}{x^2+2x}=3.20$

$3.2x^2+6.4x=384$

$3.2x^2+6.4x-384=0$

By the quadratic formula,

$x=\frac{-6.4\pm \sqrt{40.96+4915.2}}{6.4}$

$\implies x = \frac{-6.4\pm 70.4}{6.4}$

$\implies x = 10\text{ or } x = -12$

Since, the number can not be negative,

Hence, 10 soccer club members are going to the tournament.