Answer:
There are 32 pupils in the class
Step-by-step explanation:
Let's say there are N pupils in the class. Then each pupil must send N-1 cards - because it would make no sense to send one to themselves! So each of the N pupils send N-1 cards, which becomes 992 cards in total. In equation form, this is
[tex]N(N-1)=992\\N^2-N-992=0[/tex]
This is a second degree polynomial, which has the solutions
[tex]N=\frac{-b\pm \sqrt{b^2-4\cdot a \cdot c}}{2a}[/tex]
where [tex]a=1, b=-1, \text{and }c=-992[/tex]
If we insert these numbers in the equation,
[tex]N=\frac{-(-1)\pm \sqrt{1^2-4*1*(-992)}}{2*1}\\ = \frac{1\pm \sqrt{1+4*992}}{2}\\= \frac{1 \pm 63}{2}[/tex]
If we choose the solution with the minus sign, we get
N=-31
but this makes no sense! There can't be a negative number of pupils in the class!
So we choose the solution with the plus sign,
[tex]N=\frac{1+63}{2}\\ =\frac{64}{2}\\ =32[/tex]
So there are 32 pupils in the class
Answer:
number of pupils in the class = 32
Step-by-step explanation:
Let n be the number of students. So n-1 cards will be sent by each student.
n(n-1) =192
n² - n =192
n² - n - 192 = 0
n² - 32n + 31n - (31*32) = 0
n(n - 32) + 31 (n-32) = 0
(n-32)(n+31) = 0
n - 32 = 0 or n + 31 = 0
n = 32 or n = -31 is not possible because no. of students cannot be negative
n= 32
