Question

The soccer club has planned a trip to a tournament. The cost of the van is $210. When 3 students who are not members of the club join the trip, the transportation cost per person drops by $5.83. How many soccer club members are going to the tournament?

Answer 1

Answer:

The number of students who are going to the tournament are:

                                      12

Step-by-step explanation:

Let x be the number of students who were earlier going to trip.

and total cost=$ 210

Hence, the cost per person earlier was:

 $\dfrac{210}{x}$

Also, 3 more students joined the group.

This means that the cost per person now will be:

$\dfrac{210}{x+3}$

Also, it is given that:

When 3 students who are not members of the club join the trip, the transportation cost per person drops by $5.83.

This means that:

$\dfrac{210}{x+3}=\dfrac{210}{x}-5.83$

Hence,

$\dfrac{210}{x}-\dfrac{210}{x+3}=5.83$

i.e.

$\dfrac{210(x+3-x)}{x(x+3)}=5.83\\\\\\i.e.\\\\\\\dfrac{210\times 3}{x(x+3)}=5.83\\\\\\i.e.\\\\\\x(x+3)=\dfrac{630}{5.83}\\\\\\x(x+3)=108.061$

on simplifying the equation we get:

$583x^2+1749x-63000=0$

Hence, on using the quadratic formula:

i.e. any quadratic equation of the type:

$ax^2+bx+c=0$

has solution of the type:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here we have:

a= 583, b=1749 and c= -63000

Hence, on putting these value in the quadratic formula we get the value of x as:

x=9.003 and x= -12.003

Since, the students will exist as a whole and positive number.

Hence, x=9

This means that the total number of students who will be going to the tournament are: x+3=9+3=12 students.