# Kabini ubudala babantu ababini1017

Qwalasela abantu ababini $$A$$ kunye $$B$$ abangazalwanga kwangalemini inye kwaye $$A$$ bancinci kuno $$B$$ . Bonisa ukuba minye iminye iminyaka emibini yobudala $$a,b \in \mathbb{N}$$ , esebenza kuyo: $$2\cdot a = b$$ . Saqala ukuseta $$d \in \mathbb{R}^+$$ njengomahluko wobudala phakathi kwe $$A$$ kunye $$B$$ ekuzalweni kwe $$A$$ nge $$d = d_0 + d_1$$ , $$d_0 \in \mathbb{N}_0, d_1 \in \mathbb{R}, d_1 \in [0;1[$$ . Ngoku sijonga inqaku elingenakuphikiswa ngexesha $$x \in \mathbb{R}^+$$ emva kokuzalwa kwe $$A$$ nge $$x = x_0 + x_1$$ , $$x_0 \in \mathbb{N}_0, x_1 \in \mathbb{R}, x_1 \in [0;1[$$ .

Okwangoku ngeli xesha, ngokwenkcazo, $$a = \lfloor x \rfloor$$ kunye $$b = \lfloor x+d \rfloor$$ . Ngoku simisela zonke $$x$$ ezizigcinileyo:

$$2 \lfloor x \rfloor = \lfloor x+d \rfloor \Leftrightarrow 2 \lfloor x_0 + x_1 \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor$$

Ityala lokuqala: $$0 \leq x_1 + d_1 < 1$$:

Emva koko $$2 \lfloor x_0 + x_1 \rfloor = \lfloor x_0 + d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor \Leftrightarrow 2 x_0 = x_0 + d_0 \Leftrightarrow x_0 = d_0.$$

Oku kuthetha ukuba $$a = \lfloor x \rfloor = \lfloor x_0 + x_1 \rfloor = \lfloor d_0 + x_1 \rfloor = d_0$$ kwaye $$b = \lfloor x + d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor = 2 d_0$$ iqela lokuqala lobudala $$b = \lfloor x + d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + \underbrace{x_1 + d_1}_{< 1} \rfloor = 2 d_0$$ .

Ityala lesibini: $$1 \leq x_1 + d_1 < 2$$:

Emva koko $$2 \lfloor x_0 + x_1 \rfloor = \lfloor x_0 + d_0 + \underbrace{x_1 + d_1}_{\geq 1} \rfloor \Leftrightarrow 2 x_0 = x_0 + d_0 + 1 \Leftrightarrow x_0 = d_0 + 1.$$

Oku kuthetha ukuba $$a = \lfloor x \rfloor = \lfloor x_0 + x_1 \rfloor = \lfloor d_0 + 1 + x_1 \rfloor = d_0 + 1$$ yaye $$b = \lfloor x+d \rfloor = \lfloor x_0 + x_1 + d_0 + d_1 \rfloor = \lfloor 2 d_0 + 1 + \underbrace{x_1 + d_1}_{\geq 1} \rfloor = 2 d_0 + 2$$ iqela lesibini leminyaka elifunayo.

Ngokukodwa, oku kuthetha, umzekelo: Ukuba umama wakho wakuzala eneminyaka eyi- $$20$$ iminyaka, uyiphindaphindeke kabini iminyaka yakho $$40$$ kunye $$42$$ iminyaka. Kunika umdla ukuba kwaye nini na $$n$$ amaxesha amdala: Nantsi $$n \in \mathbb{N}$$ ngokungafanelekanga kwaye sifumana $$x_0 = \frac{d_0}{n-1} \in \mathbb{N} \Leftrightarrow d_0 = k (n-1)$$ . Oku kusebenza kanye xa umahluko wobudala obupheleleyo $$\lfloor d \rfloor = d_0$$ nge $$n-1$$ , o.k.t. kwimeko engentla umama wakho $$24$$ iminyaka $$6$$ amaxesha akho eminyaka.

Emva