Question Number 206045 by mr W last updated on 05/Apr/24
Commented by mr W last updated on 05/Apr/24
$${a}\:{special}\:{case}\:{of}\:{Q}\mathrm{206053} \\ $$
Answered by HeferH24 last updated on 05/Apr/24
$$\:{A}+{E}\:=\:{F}+{B}\:\:\:...\:\left(+\right) \\ $$$$\:{F}+{D}\:=\:{E}+{C}\: \\ $$$$\:\left({F}+{E}\:=\:\mathrm{21}\right) \\ $$$$\:{A}+{D}\:=\:{B}+{C} \\ $$$$\: \\ $$$$\:{A}+\mathrm{9}\:+\:{x}\:+\:{D}\:=\:{E}+{F}+{C}+{B}\: \\ $$$$\:\mathrm{9}+{x}\:=\:\mathrm{21} \\ $$$$\:{x}\:=\:\mathrm{12} \\ $$
Commented by HeferH24 last updated on 05/Apr/24
Commented by mr W last updated on 05/Apr/24
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Answered by A5T last updated on 07/Apr/24
![9+[BGE]+x+[HFD]=21+[AGF]+[EHC]..(i) 9+[AGF]+x+[HEC]=21+[BGE]+[HFD]..(ii) (i)−(ii): [BGE]−[AGF]+[HFD]−[HEC] =[AGF]−[BGE]+[EHC]−[HFD] ⇒[BGE]+[HFD]=[AGF]+[HEC] into (i) ⇒9+x=21⇒x=12](Q206100.png)
$$\mathrm{9}+\left[{BGE}\right]+{x}+\left[{HFD}\right]=\mathrm{21}+\left[{AGF}\right]+\left[{EHC}\right]..\left({i}\right) \\ $$$$\mathrm{9}+\left[{AGF}\right]+{x}+\left[{HEC}\right]=\mathrm{21}+\left[{BGE}\right]+\left[{HFD}\right]..\left({ii}\right) \\ $$$$\left({i}\right)−\left({ii}\right):\:\left[{BGE}\right]−\left[{AGF}\right]+\left[{HFD}\right]−\left[{HEC}\right] \\ $$$$=\left[{AGF}\right]−\left[{BGE}\right]+\left[{EHC}\right]−\left[{HFD}\right] \\ $$$$\Rightarrow\left[{BGE}\right]+\left[{HFD}\right]=\left[{AGF}\right]+\left[{HEC}\right]\:{into}\:\left({i}\right) \\ $$$$\Rightarrow\mathrm{9}+{x}=\mathrm{21}\Rightarrow{x}=\mathrm{12} \\ $$