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

Answer:

10

Step-by-step 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 = $p=\frac{192}{N}$  --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: $p-3.20 = \frac{192}{N+2}$  ---B

Using A

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

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

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

$\frac{192N+384-192N}{N(N+2)}=3.20$

$\frac{384}{N(N+2)}=3.20$

$\frac{384}{3.20}=N(N+2)$

$120=N^2+2N$

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

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

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

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

$N=-12,10$

Since number of members cannot be negative .

So, the number of members is 10 .

Hence there are 10 members in the club.