Réitigh 1/c_{T}=1/2+1/9+1/2+frac{1}{6}+frac{1}{12}

$$\frac { 1 } { c _ { T } } = \frac { 1 } { 2 } + \frac { 1 } { 9 } + \frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 12 }$$

Réitigh do c_T.

$$c_{T}=\frac{36}{49}\approx 0.734693878$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Ní féidir leis an athróg c_{T} a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Iolraigh an dá thaobh den chothromóid faoi 36c_{T}, an comhiolraí is lú de c_{T},2,9,6,12.

$$36=36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Méadaigh 36 agus \frac{1}{2} chun \frac{36}{2} a fháil.

$$36=\frac{36}{2}c_{T}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Roinn 36 faoi 2 chun 18 a fháil.

$$36=18c_{T}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Méadaigh 36 agus \frac{1}{9} chun \frac{36}{9} a fháil.

$$36=18c_{T}+\frac{36}{9}c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Roinn 36 faoi 9 chun 4 a fháil.

$$36=18c_{T}+4c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Comhcheangail 18c_{T} agus 4c_{T} chun 22c_{T} a fháil.

$$36=22c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Méadaigh 36 agus \frac{1}{2} chun \frac{36}{2} a fháil.

$$36=22c_{T}+\frac{36}{2}c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Roinn 36 faoi 2 chun 18 a fháil.

$$36=22c_{T}+18c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Comhcheangail 22c_{T} agus 18c_{T} chun 40c_{T} a fháil.

$$36=40c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Méadaigh 36 agus \frac{1}{6} chun \frac{36}{6} a fháil.

$$36=40c_{T}+\frac{36}{6}c_{T}+36c_{T}\times \frac{1}{12}$$

Roinn 36 faoi 6 chun 6 a fháil.

$$36=40c_{T}+6c_{T}+36c_{T}\times \frac{1}{12}$$

Comhcheangail 40c_{T} agus 6c_{T} chun 46c_{T} a fháil.

$$36=46c_{T}+36c_{T}\times \frac{1}{12}$$

Méadaigh 36 agus \frac{1}{12} chun \frac{36}{12} a fháil.

$$36=46c_{T}+\frac{36}{12}c_{T}$$

Roinn 36 faoi 12 chun 3 a fháil.

$$36=46c_{T}+3c_{T}$$

Comhcheangail 46c_{T} agus 3c_{T} chun 49c_{T} a fháil.

$$36=49c_{T}$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$49c_{T}=36$$

Roinn an dá thaobh faoi 49.

$$c_{T}=\frac{36}{49}$$