2007 Cyprus MO/Lyceum/Problem 26

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Problem

The number of boys in a school is 3 times the number of girls and the number of girls is 9 times the number of teachers. Let us denote with $b$, $g$ and $t$, the number of boys, girls and teachers respectively. Then the total number of boys, girls and teachers equals to

$\mathrm{(A) \ } 31b\qquad \mathrm{(B) \ } \frac{37b}{27}\qquad \mathrm{(C) \ } 13g\qquad \mathrm{(D) \ } \frac{37g}{27}\qquad \mathrm{(E) \ } \frac{37t}{27}$

Solution

$g=\frac{b}3$ and $t=\frac{b}{27}$

$S=b+\frac{b}{3}+\frac{b}{27}=\frac{37b}{27}\Rightarrow\mathrm{ B}$

See also

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