Question Number 212085 by hardmath last updated on 28/Sep/24
$$\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\mathbb{N} \\ $$$$\mathrm{5a}\:+\:\mathrm{6b}\:+\:\mathrm{7c}\:=\:\mathrm{70} \\ $$$$\mathrm{find}:\:\:\mathrm{max}\left(\mathrm{a}\right)\:=\:? \\ $$
Commented by Frix last updated on 28/Sep/24
$$\mathrm{If}\:\mathrm{0}\in\mathbb{N}\:\Rightarrow\:\mathrm{max}\:{a}\:=\mathrm{14}\:\:\:\:\:\left({b}={c}=\mathrm{0}\right) \\ $$$$\mathrm{If}\:\mathrm{0}\notin\mathbb{N}\:\Rightarrow\:\mathrm{max}\:{a}\:=\mathrm{10}\:\:\:\:\:\left({b}=\mathrm{1}\wedge{c}=\mathrm{2}\right) \\ $$