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 = [tex]\frac{192}{x}[/tex]
⇒ The cost of transportation of (x+2) student = [tex]\frac{192}{x-2}[/tex]
According to the question,
[tex]\frac{192}{x}-\frac{192}{x+2}=3.20[/tex]
[tex]192(\frac{1}{x}-\frac{1}{x+2})=3.20[/tex]
[tex]192(\frac{x+2-x}{x(x+2)})=3.20[/tex]
[tex]\frac{384}{x^2+2x}=3.20[/tex]
[tex]3.2x^2+6.4x=384[/tex]
[tex]3.2x^2+6.4x-384=0[/tex]
By the quadratic formula,
[tex]x=\frac{-6.4\pm \sqrt{40.96+4915.2}}{6.4}[/tex]
[tex]\implies x = \frac{-6.4\pm 70.4}{6.4}[/tex]
[tex]\implies x = 10\text{ or } x = -12[/tex]
Since, the number can not be negative,
Hence, 10 soccer club members are going to the tournament.
