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

10 soccer club members are going to the tournament.

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 =
`(192)/(x)`

⇒ The cost of transportation of (x+2) student =
`(192)/(x-2)`

According to the question,

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

`192((1)/(x)-(1)/(x+2))=3.20`

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

`(384)/(x^2+2x)=3.20`

`3.2x^2+6.4x=384`

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

By the quadratic formula,

`x=(-6.4\pm √(40.96+4915.2))/(6.4)`

`\implies x = (-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.