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Question Number 10076 by konen last updated on 23/Jan/17

3a=4b=5c  2a+3b−c=146  ⇒c=?

$$\mathrm{3a}=\mathrm{4b}=\mathrm{5c} \\ $$$$\mathrm{2a}+\mathrm{3b}−\mathrm{c}=\mathrm{146} \\ $$$$\Rightarrow\mathrm{c}=? \\ $$

Answered by ridwan balatif last updated on 23/Jan/17

3a=5c→a=(5/3)c  4b=5c→b=(5/4)c  2a+3b−c=146  2((5/3)c)+3((5/4)c)−c=146  ((73)/(12))c=146  c=2

$$\mathrm{3a}=\mathrm{5c}\rightarrow\mathrm{a}=\frac{\mathrm{5}}{\mathrm{3}}\mathrm{c} \\ $$$$\mathrm{4b}=\mathrm{5c}\rightarrow\mathrm{b}=\frac{\mathrm{5}}{\mathrm{4}}\mathrm{c} \\ $$$$\mathrm{2a}+\mathrm{3b}−\mathrm{c}=\mathrm{146} \\ $$$$\mathrm{2}\left(\frac{\mathrm{5}}{\mathrm{3}}\mathrm{c}\right)+\mathrm{3}\left(\frac{\mathrm{5}}{\mathrm{4}}\mathrm{c}\right)−\mathrm{c}=\mathrm{146} \\ $$$$\frac{\mathrm{73}}{\mathrm{12}}\mathrm{c}=\mathrm{146} \\ $$$$\mathrm{c}=\mathrm{2} \\ $$

Answered by ridwan balatif last updated on 23/Jan/17

another way  2a+3b−c=146  −−−−−−−−−×12  24a+36b−12c=146×12  8(3a+4b)+4b−12c=146×12  8(5c+5c)+5c−12c=146×12  73c=146×12  c=24

$$\mathrm{another}\:\mathrm{way} \\ $$$$\mathrm{2a}+\mathrm{3b}−\mathrm{c}=\mathrm{146} \\ $$$$−−−−−−−−−×\mathrm{12} \\ $$$$\mathrm{24a}+\mathrm{36b}−\mathrm{12c}=\mathrm{146}×\mathrm{12} \\ $$$$\mathrm{8}\left(\mathrm{3a}+\mathrm{4b}\right)+\mathrm{4b}−\mathrm{12c}=\mathrm{146}×\mathrm{12} \\ $$$$\mathrm{8}\left(\mathrm{5c}+\mathrm{5c}\right)+\mathrm{5c}−\mathrm{12c}=\mathrm{146}×\mathrm{12} \\ $$$$\mathrm{73c}=\mathrm{146}×\mathrm{12} \\ $$$$\mathrm{c}=\mathrm{24} \\ $$

Commented by konen last updated on 23/Jan/17

thank you♥

$$\mathrm{thank}\:\mathrm{you}\heartsuit \\ $$

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