Classroom Confusion!
Algebra
Level
2
There are 10 girls in a mixed class.
If two pupils from the class are selected at random, then the probability that both are girls is 0.15
How many boys are in the class?
23
12
63
15
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Let the number of boys in the class be x.
Hence 1010+x×99+x=0.15=320.
Simplifying gives 1800=3(10+x)(9+x) and then x2+19x−510=0.
Factorising gives (x+34)(x−15)=0 and, since x≠−34, x=15.
Alternatively, let the number of students in the class be x.
Hence 10x×9x−1=0.15=320.
Simplifying gives 600=x(x−1) and then x2−x−600=0.
Factorising gives (x+24)(x−25)=0 and, since x≠−24, x=25.
Therefore the number of boys in the class is 15.