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Question Number 193756 by Shlock last updated on 19/Jun/23

Answered by talminator2856792 last updated on 19/Jun/23

$$7(7a+b)+c=7\left(40\right)+6$$$$$$$$\to c=6\left(\mathrm{mod}7\right)$$$$\to c=6$$$$$$$$7a+b=40$$$$\mathrm{since}b\mathrm{is}\mathrm{one}\mathrm{digit},$$$$\mathrm{difference}\mathrm{between}40\mathrm{and}40-b\mathrm{is}$$$$\mathrm{a}\mathrm{multiple}\mathrm{of}7\mathrm{not}\mathrm{greater}\mathrm{than}9;$$$$\mathrm{only}7\times 1\mathrm{applies}.$$$$\to b=40-7\times \lfloor \frac{40}{7}\rfloor$$$$b=5$$$$$$$$\to a=\lfloor \frac{40}{7}\rfloor$$$$a=5$$$$$$$$cba-abc=655-556$$$$=99$$

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