Question Number 120196 by ZiYangLee last updated on 30/Oct/20
$$\mathrm{The}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{male}\:\mathrm{and}\:\mathrm{female}\:\mathrm{participants} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{competition}\:\mathrm{is}\:\mathrm{3}:\mathrm{2}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{15\%}\: \\ $$$$\mathrm{of}\:\mathrm{participants}\:\mathrm{are}\:\mathrm{prize}\:\mathrm{winner},\:\mathrm{and}\:\mathrm{among} \\ $$$$\mathrm{the}\:\mathrm{prize}\:\mathrm{winner},\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{male}\:\mathrm{to}\:\mathrm{female} \\ $$$$\mathrm{is}\:\mathrm{2}:\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{male}\:\mathrm{and}\:\mathrm{female} \\ $$$$\mathrm{among}\:\mathrm{the}\:\mathrm{participants}\:\mathrm{that}\:\mathrm{are}\:\mathrm{not}\:\mathrm{prize} \\ $$$$\mathrm{winner}. \\ $$
Answered by benjo_mathlover last updated on 30/Oct/20
$${male}\::\:{female}\:=\:\mathrm{3}:\mathrm{2}\:\begin{cases}{{male}=\mathrm{3}{k}}\\{{female}=\mathrm{2}{k}}\end{cases}\:{Total}=\mathrm{5}{k} \\ $$$${are}\:{prize}\:{winner}\:=\:\frac{\mathrm{15}}{\mathrm{100}}×\mathrm{5}{k}\:=\:\frac{\mathrm{3}}{\mathrm{4}}{k} \\ $$$${male}\:{prize}\:{winner}\:=\:\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{3}}{\mathrm{4}}{k}=\frac{\mathrm{1}}{\mathrm{2}}{k} \\ $$$${female}\:{prize}\:{winner}\:=\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{3}}{\mathrm{4}}{k}=\frac{\mathrm{1}}{\mathrm{4}}{k} \\ $$$${male}\:{non}\:{prize}\:{winner}=\mathrm{3}{k}−\frac{\mathrm{1}}{\mathrm{2}}{k}=\frac{\mathrm{5}}{\mathrm{2}}{k} \\ $$$${female}\:{non}\:{prize}\:{winner}=\mathrm{2}{k}−\frac{\mathrm{1}}{\mathrm{4}}{k}=\frac{\mathrm{7}}{\mathrm{4}}{k} \\ $$$${then}\:\frac{{male}\:{non}\:{prize}}{{female}\:{non}\:{prize}}\:=\:\frac{\mathrm{5}/\mathrm{2}}{\mathrm{7}/\mathrm{4}} \\ $$$$=\:\frac{\mathrm{5}}{\mathrm{2}}×\frac{\mathrm{4}}{\mathrm{7}}=\frac{\mathrm{10}}{\mathrm{7}}\:\: \\ $$
Commented by ZiYangLee last updated on 30/Oct/20
$$\bigstar\bigstar \\ $$