Whakaoti i te c-0/100-0=20-x/180-x-x

$$\frac{ c-0 }{ 100-0 } = \frac{ 20-x }{ 180-x-x }$$

Whakaoti mō c

$$c=-\frac{50\left(x-20\right)}{90-x}$$

$$x\neq 90$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 2\left(-x+90\right).

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)\left(c-0\right)=20-x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{50}x+\frac{9}{5} ki te c-0.

$$-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)=20-x$$

Whakaraupapatia anō ngā kīanga tau.

$$-\frac{1}{50}cx+\frac{9}{5}c=-x+20$$

Pahekotia ngā kīanga tau katoa e whai ana i te c.

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)c=-x+20$$

He hanga arowhānui tō te whārite.

$$\left(-\frac{x}{50}+\frac{9}{5}\right)c=20-x$$

Whakawehea ngā taha e rua ki te -\frac{1}{50}x+\frac{9}{5}.

$$\frac{\left(-\frac{x}{50}+\frac{9}{5}\right)c}{-\frac{x}{50}+\frac{9}{5}}=\frac{20-x}{-\frac{x}{50}+\frac{9}{5}}$$

Mā te whakawehe ki te -\frac{1}{50}x+\frac{9}{5} ka wetekia te whakareanga ki te -\frac{1}{50}x+\frac{9}{5}.

$$c=\frac{20-x}{-\frac{x}{50}+\frac{9}{5}}$$

Whakawehe -x+20 ki te -\frac{1}{50}x+\frac{9}{5}.

$$c=\frac{50\left(20-x\right)}{90-x}$$

Whakaoti mō x

$$x=-\frac{10\left(9c-100\right)}{50-c}$$

$$c\neq 50$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 90 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 2\left(-x+90\right).

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)\left(c-0\right)=20-x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{50}x+\frac{9}{5} ki te c-0.

$$-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)=20-x$$

Me tāpiri te x ki ngā taha e rua.

$$-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)+x=20$$

Tangohia te \frac{9}{5}\left(c-0\right) mai i ngā taha e rua.

$$-\frac{1}{50}x\left(c-0\right)+x=20-\frac{9}{5}\left(c-0\right)$$

Whakaraupapatia anō ngā kīanga tau.

$$-\frac{1}{50}cx+x=20-\frac{9}{5}c$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-\frac{1}{50}c+1\right)x=20-\frac{9}{5}c$$

He hanga arowhānui tō te whārite.

$$\left(-\frac{c}{50}+1\right)x=-\frac{9c}{5}+20$$

Whakawehea ngā taha e rua ki te -\frac{1}{50}c+1.

$$\frac{\left(-\frac{c}{50}+1\right)x}{-\frac{c}{50}+1}=\frac{-\frac{9c}{5}+20}{-\frac{c}{50}+1}$$

Mā te whakawehe ki te -\frac{1}{50}c+1 ka wetekia te whakareanga ki te -\frac{1}{50}c+1.

$$x=\frac{-\frac{9c}{5}+20}{-\frac{c}{50}+1}$$

Whakawehe 20-\frac{9c}{5} ki te -\frac{1}{50}c+1.

$$x=\frac{10\left(100-9c\right)}{50-c}$$

Tē taea kia ōrite te tāupe x ki 90.

$$x=\frac{10\left(100-9c\right)}{50-c}\text{, }x\neq 90$$