Whakaoti i te 21%=x+(x-78%)*1025

$$21 \% = x + ( x - 78 \% ) \times 1025$$

Whakaoti mō x

$$x=\frac{1403}{1800}\approx 0.779444444$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{78}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{21}{100}=x+\left(x-\frac{39}{50}\right)\times 1025$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-\frac{39}{50} ki te 1025.

$$\frac{21}{100}=x+1025x-\frac{39}{50}\times 1025$$

Tuhia te -\frac{39}{50}\times 1025 hei hautanga kotahi.

$$\frac{21}{100}=x+1025x+\frac{-39\times 1025}{50}$$

Whakareatia te -39 ki te 1025, ka -39975.

$$\frac{21}{100}=x+1025x+\frac{-39975}{50}$$

Whakahekea te hautanga \frac{-39975}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\frac{21}{100}=x+1025x-\frac{1599}{2}$$

Pahekotia te x me 1025x, ka 1026x.

$$\frac{21}{100}=1026x-\frac{1599}{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$1026x-\frac{1599}{2}=\frac{21}{100}$$

Me tāpiri te \frac{1599}{2} ki ngā taha e rua.

$$1026x=\frac{21}{100}+\frac{1599}{2}$$

Ko te maha noa iti rawa atu o 100 me 2 ko 100. Me tahuri \frac{21}{100} me \frac{1599}{2} ki te hautau me te tautūnga 100.

$$1026x=\frac{21}{100}+\frac{79950}{100}$$

Tā te mea he rite te tauraro o \frac{21}{100} me \frac{79950}{100}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$1026x=\frac{21+79950}{100}$$

Tāpirihia te 21 ki te 79950, ka 79971.

$$1026x=\frac{79971}{100}$$

Whakawehea ngā taha e rua ki te 1026.

$$x=\frac{\frac{79971}{100}}{1026}$$

Tuhia te \frac{\frac{79971}{100}}{1026} hei hautanga kotahi.

$$x=\frac{79971}{100\times 1026}$$

Whakareatia te 100 ki te 1026, ka 102600.

$$x=\frac{79971}{102600}$$

Whakahekea te hautanga \frac{79971}{102600} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 57.

$$x=\frac{1403}{1800}$$