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Question Number 112804 by Aina Samuel Temidayo last updated on 09/Sep/20

$$\mathrm{If}\frac{97}{19}=\mathrm{a}+\frac{1}{\mathrm{b}+\frac{1}{\mathrm{c}}},\mathrm{where}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}\mathrm{are}$$$$\mathrm{positive}\mathrm{integers},\mathrm{then}\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{sum}$$$$\mathrm{of}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}?$$

Answered by nimnim last updated on 09/Sep/20

$$\frac{97}{19}=5+\frac{2}{19}=5+\frac{1}{\frac{19}{2}}=5+\frac{1}{9+\frac{1}{2}}$$$$\Rightarrow \mathrm{a}=5,\mathrm{b}=9,\mathrm{c}=2$$$$\therefore (\mathrm{a}+\mathrm{b}+\mathrm{c})=16★$$

Commented by Aina Samuel Temidayo last updated on 09/Sep/20

$$\mathrm{Thanks}.$$

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