Respuesta :
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:
 [tex]\dfrac{210}{x}[/tex]
Also, 3 more students joined the group.
This means that the cost per person now will be:
[tex]\dfrac{210}{x+3}[/tex]
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:
[tex]\dfrac{210}{x+3}=\dfrac{210}{x}-5.83[/tex]
Hence,
[tex]\dfrac{210}{x}-\dfrac{210}{x+3}=5.83[/tex]
i.e.
[tex]\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[/tex]
on simplifying the equation we get:
[tex]583x^2+1749x-63000=0[/tex]
Hence, on using the quadratic formula:
i.e. any quadratic equation of the type:
[tex]ax^2+bx+c=0[/tex]
has solution of the type:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
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.
