Question

The students of a class were asked to vote for one movie they would like to watch. They were given two options:
'The Lion King' and 'Frozen'. each students was given a chance to vote only once.
2/3 of the students voted for 'The Lion King' while 12 students voted for 'Frozen'.
All the students took part in the voting.
What is the total number of students in the class?

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

Answer 2

The total number of students in the class is 36

Given:

The students of a class were asked to vote for one movie they would like.

The No. of students voted for 'The Lion King' = 2/3 of class

The No. of students voted for Frozen = 12

All the students took part in the voting.

To find:

What is the total number of students in the class?

Solution:

Let x be the number of class students

The No. of students voted for 'The Lion King' = 2/3 of class

The No. of students voted for 'The Lion King' = 2/3 of x = $\frac{2x}{3}$

If  $\frac{2x}{3}$ students are voted for 'The Lion King'  

The No. of students voted for Frozen will be = x - $\frac{2x}{3}$ = $\frac{x}{3}$  

From given data the No of students voted for Frozen = 12

⇒  $\frac{x}{3}$ = 12

⇒ x = 36

The total number of students in the class = 36

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