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Weekly Problem 45 - 2012

Stage: 4 Challenge Level: Challenge Level:1

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 these solutions.

This problem is taken from the UKMT Mathematical Challenges.

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