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Question Number 191323 by Mingma last updated on 23/Apr/23

Answered by mr W last updated on 23/Apr/23

$$\frac{A}{A+B}={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$$$$\frac{A}{A+B+C}={\left(\frac{1}{3}\right)}^2=\frac{1}{9}$$$$\Rightarrow A=\frac{A+B+C}{9}$$$$\Rightarrow A+B=4A\Rightarrow B=3A=\frac{3(A+B+C)}{9}$$$$\Rightarrow C=(1-\frac{1}{9}-\frac{3}{9})(A+B+C)=\frac{5(A+B+C)}{9}$$$$\Rightarrow A:B:C=1:3:5$$

Commented by Mingma last updated on 23/Apr/23

Excellent!

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