Weekly Problem 45

9432 /www/nrich/html/content/id/9432/ 1 2012-09-18T12:19:44 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> 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? If you liked this problem, <a href="/7221">here is an NRICH task</a> which challenges you to use similar mathematical ideas. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Let the number of boys in the class be $x$. Hence $\frac{10}{10+x}\times\frac{9}{9+x} = 0.15 = \frac{3}{20}$. Simplifying gives $1800=3(10+x)(9+x)$ and then $x^{2}+19x-510=0$. Factorising gives $(x+34)(x-15)=0$ and, since $x\not=-34$, $x=15$. Alternatively, let the number of students in the class be $x$. Hence $\frac{10}{x}\times\frac{9}{x-1} = 0.15 = \frac{3}{20}$. Simplifying gives $600=x(x-1)$ and then $x^{2}-x-600=0$. Factorising gives $(x+24)(x-25)=0$ and, since $x\not=-24$, $x=25$. Therefore the number of boys in the class is 15. Students from Comberton Village College sent us <a href="/content/id/9432/Weekly45solution.pdf">these solutions</a>. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Probability - Stage 4 Short Problem, UKMT 2010-2011 p 108 Q20</mdoxml> 2 3 0 0 0 1 0 Weekly Problem 45 - 2012 There are 10 girls in a mixed class. If two pupils are selected, the probability that they are both girls is 0.15. How many boys are in the class? Secondary Mapping Document Probability US Secondary Mapping Document Expanding and factorising quadratics Secondary Mapping Document DisplayCabinet