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Question Number 182928 by yaslm last updated on 16/Dec/22

Answered by manolex last updated on 16/Dec/22

$$A+B=1040-C$$$$\frac{A+B}{B}=\frac{11}{6}\frac{B+C}{B}=\frac{4}{3}$$$$\frac{1040-C}{B}=\frac{11}{6}B+C=\frac{4B}{3}$$$$\frac{1040-(B-C)}{B}=\frac{5}{6}$$$$1040-\frac{4B}{3}=\frac{5B}{6}$$$$1040=\frac{13B}{6}$$$$B=480$$$$A=\frac{5B}{6}=400$$$$C=\frac{B}{3}=160$$$$C.S=(A,B,C)=(400,480,160)$$$$$$$$$$$$$$

Answered by HeferH last updated on 17/Dec/22

$$\frac{A}{B}=\frac{5k}{6k}\Rightarrow \frac{C}{B}=\frac{2k}{6k}$$$$5k+6k+2k=1040$$$$k=80$$$$A=400;B=480;C=160$$

Answered by Rasheed.Sindhi last updated on 17/Dec/22

$$\overline{)\begin{array}{ccc}A& B& C\\ 5& 6& \\ & 3& 1\\ 5& 6& 2\end{array}}$$$$A:B:C=5:6:2$$$$A+B+C=5k+6k+2k=13k=1040$$$$k=\frac{1040}{13}=80$$$$A=5\times 80=400$$$$B=6\times 80=480$$$$C=2\times 80=\underset{-}{160}$$$$1040$$

Answered by Rasheed.Sindhi last updated on 17/Dec/22

$$\frac{A}{B}=\frac{5}{6}\Rightarrow \frac{A}{5}=\frac{B}{6}$$$$\frac{C}{B}=\frac{1}{3}\Rightarrow \frac{C}{1}=\frac{B}{3}\Rightarrow \frac{C}{2}=\frac{B}{6}$$$$\frac{A}{5}=\frac{B}{6}=\frac{C}{2}=\frac{A+B+C}{5+6+2}=\frac{1040}{13}=80$$$$A=5\times 80=400$$$$B=6\times 80=480$$$$C=2\times 80=\underset{-}{160}$$$$1040$$

Answered by Rasheed.Sindhi last updated on 17/Dec/22

$$\underset{\left(i\right)}{\underbrace{\frac{A}{B}=\frac{5}{6}}},\underset{\left(ii\right)}{\underbrace{\frac{C}{B}=\frac{1}{3}}},A+B+C=1040$$$$\left(i\right)\Rightarrow \frac{A+B}{B}=\frac{5+6}{6}\left[Componendo\right]$$$$\Rightarrow \frac{A+B}{B}=\frac{11}{6}.....\left(iii\right)$$$$\left(iii\right)+\left(ii\right):\frac{A+B+C}{B}=\frac{11}{6}+\frac{1}{3}$$$$\frac{1040}{B}=\frac{13}{6}\Rightarrow B=\frac{1040\times 6}{13}=480$$$$\left(i\right)\Rightarrow \frac{A}{480}=\frac{5}{6}\Rightarrow A=\frac{5\times 480}{6}=400$$$$\left(ii\right)\Rightarrow \frac{C}{480}=\frac{1}{3}\Rightarrow C=\frac{480}{3}=160$$

Answered by Rasheed.Sindhi last updated on 17/Dec/22

$$$$$$\underset{\left(i\right)}{\underbrace{\frac{A}{B}=\frac{5}{6}}},\underset{\left(ii\right)}{\underbrace{\frac{C}{B}=\frac{1}{3}}},A+B+C=1040$$$$\left(i\right)+\left(ii\right):\frac{A+C}{B}=\frac{7}{6}$$$$\frac{A+C+B}{B}=\frac{7+6}{6}\left[Componendo\right]$$$$\frac{1040}{B}=\frac{13}{6}\Rightarrow B=\frac{1040\times 6}{13}=480$$$$\left(i\right)\Rightarrow \frac{A}{480}=\frac{5}{6}\Rightarrow A=\frac{480\times 5}{6}=400$$$$\left(ii\right)\Rightarrow \frac{C}{480}=\frac{1}{3}\Rightarrow C=\frac{480\times 1}{3}=160$$

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