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Question Number 205471 by Fridunatjan08 last updated on 21/Mar/24

$$Solvetheequation:\frac{x}{21}+\frac{x}{77}+\frac{x}{165}+\frac{x}{285}=200$$

Answered by Rasheed.Sindhi last updated on 23/Mar/24

$$\frac{x}{21}+\frac{x}{77}+\frac{x}{165}+\frac{x}{285}=200$$$$x(\frac{1}{21}+\frac{1}{77}+\frac{1}{165}+\frac{1}{285})=200$$$$x(\frac{1}{7}(\frac{1}{3}+\frac{1}{11})+\frac{1}{15}(\frac{1}{11}+\frac{1}{19}))=200$$$$x(\frac{1}{\cancel{\underset{1}{7}}}\left(\frac{\cancel{\stackrel{2}{14}}}{3\times 11}\right)+\frac{1}{\cancel{\underset{1}{15}}}\left(\frac{\cancel{\stackrel{2}{30}}}{11\times 19}\right))=200$$$$x(\frac{1}{33}+\frac{1}{209})=100$$$$x\left(\frac{1}{11}(\frac{1}{3}+\frac{1}{19})\right)=100$$$$x\left(\frac{1}{\cancel{\underset{1}{11}}}\left(\frac{\cancel{\stackrel{2}{22}}}{3\times 19}\right)\right)=100$$$$x\left(\frac{1}{57}\right)=50$$$$x=50\times 57=2850$$

Answered by Rasheed.Sindhi last updated on 22/Mar/24

$$Similarmethod\left(groupinginanotherway\right)$$$$\frac{x}{21}+\frac{x}{285}+\frac{x}{77}+\frac{x}{165}=200$$$$\frac{1}{3}(\frac{x}{7}+\frac{x}{95})+\frac{1}{11}(\frac{x}{7}+\frac{x}{15})=200$$$$\frac{1}{\cancel{3}}\cdot \frac{\cancel{\stackrel{34}{102}}x}{665}+\frac{1}{\cancel{11}}\cdot \frac{\cancel{\stackrel{2}{22}}x}{105}=200$$$$\frac{17x}{665}+\frac{x}{105}=100$$$$\frac{1}{35}(\frac{17x}{19}+\frac{x}{3})=100$$$$\frac{1}{\cancel{35}}\left(\frac{\cancel{\stackrel{2}{70}}x}{57}\right)=100$$$$\frac{x}{57}=50\Rightarrow x=2850$$

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