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, the transportation cost per person drops by $3.20. How many soccer club members are going to the tournament?

Answer 1

10

Explanation:

Let N be the number of members of club.

The cost of the van is $192.

Let p be the cost per person

So,Cost per person =
`p=(192)/(N)` --A

Now we are given that When 2 students who are not members of the club join the trip, the transportation cost per person drops by $3.20.

So, equation becomes:
`p-3.20 = (192)/(N+2)` ---B

Using A

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

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

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

`(192N+384-192N)/(N(N+2))=3.20`

`(384)/(N(N+2))=3.20`

`(384)/(3.20)=N(N+2)`

`120=N^2+2N`

`N^2+2N-120=0`

`N^2+12N-10N-120=0`

`N(N+12)-10(N+12)=0`

`(N+12)(N-10)=0`

`N=-12,10`

Since number of members cannot be negative .

So, the number of members is 10 .

Hence there are 10 members in the club.