Knowing the right Ratio

Algebra Level pending

In a class, 32 students are boys. Each boy knows five girls and each girl knows eight boys. What is the smallest number of girls possible in the class?

Note: "Knows" means they know each other.

5 8 20 37 169 1

Achmad Damanhuri by Achmad Damanhuri , 26, Indonesia

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1 solution

Each group of 8 8 boys "knows" the same 5 5 girls in minimum. Hence 32 32 boys "knows" 32 8 × 5 = 20 \dfrac{32}{8}\times 5=\boxed {20} girls, which gives the required minimum.

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