Question Number 171397 by mathlove last updated on 14/Jun/22
$${ax}+{by}+{cz}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${x}+{y}+{z}=\mathrm{18} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=? \\ $$
Commented by mr W last updated on 14/Jun/22
$$\mathrm{2}\:{equations}\:{for}\:\mathrm{6}\:{variables},\: \\ $$$$\Rightarrow{you}\:{can}\:{get}\:{any}\:{value}\:{for}\:{a},{b},{c}. \\ $$
Commented by mr W last updated on 14/Jun/22
$${did}\:{you}\:{create}\:{the}\:{questions}\:{or}\:{you} \\ $$$${got}\:{them}\:{somewhere}? \\ $$
Commented by MJS_new last updated on 15/Jun/22
$$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{mathematics},\:\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{game} \\ $$$$\mathrm{let}\:{a}={b}={c}=\frac{\mathrm{1}}{\mathrm{27}} \\ $$$$\Rightarrow\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=\mathrm{81} \\ $$