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Question Number 167828 by otchereabdullai@gmail.com last updated on 26/Mar/22

$$\mathrm{Houses}\mathrm{on}\mathrm{one}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{particular}$$$$\mathrm{street}\mathrm{are}\mathrm{assigned}\mathrm{odd}\mathrm{numbers},$$$$\mathrm{starting}\mathrm{from}11.\mathrm{If}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}$$$$\mathrm{numbers}\mathrm{is}551,\mathrm{how}\mathrm{many}\mathrm{houses}$$$$\mathrm{are}\mathrm{there}?$$

Answered by mr W last updated on 27/Mar/22

$$saytherearenhouses.$$$$thefirst{house}^{\prime }snumber=11$$$$thelast{house}^{\prime }snumber=11+2(n-1)$$$$sumofnumbersofallhouses:$$$$\frac{n(11+11+2(n-1))}{2}=551$$$$n^2+10n-551=0$$$$(n-19)(n+29)=0$$$$\Rightarrow n=19$$$$\Rightarrow n=-29\left(reject\right)$$

Commented by otchereabdullai@gmail.com last updated on 27/Mar/22

$$\mathrm{supper}\mathrm{prof}\mathrm{W}\mathrm{God}\mathrm{bless}\mathrm{you}!$$

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