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Question Number 211861 by hardmath last updated on 22/Sep/24

$$\overline{\mathrm{ab}}+\overline{\mathrm{ba}}=4\mathrm{c}$$$$\mathrm{a}+\mathrm{b}+3\mathrm{c}=?$$

Answered by A5T last updated on 22/Sep/24

$$10a+b+10b+a=11(a+b)=4c$$$$a+b=4k⩽9+9=18\Rightarrow k⩽4$$$$\Rightarrow 44k=4c\Rightarrow c=11k⩽44\Rightarrow c\in (11,22,33,44)$$$$whenc=11;a+b=4\Rightarrow a+b+3c=37$$$$whenc=22;a+b=8\Rightarrow a+b+3c=74$$$$whenc=33;a+b=12\Rightarrow a+b+3c=111$$$$whenc=44;a+b=16\Rightarrow a+b+3c=148$$

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