Whakaoti i te 112%=beta(12%-4%)+4%

$$112 \% = \beta ( 12 \% - 4 \% ) + 4 \%$$

Whakaoti mō β

$$\beta =\frac{27}{2}=13.5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{112}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{28}{25}=\beta \left(\frac{12}{100}-\frac{4}{100}\right)+\frac{4}{100}$$

Whakahekea te hautanga \frac{12}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{28}{25}=\beta \left(\frac{3}{25}-\frac{4}{100}\right)+\frac{4}{100}$$

Whakahekea te hautanga \frac{4}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{28}{25}=\beta \left(\frac{3}{25}-\frac{1}{25}\right)+\frac{4}{100}$$

Tā te mea he rite te tauraro o \frac{3}{25} me \frac{1}{25}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{28}{25}=\beta \times \frac{3-1}{25}+\frac{4}{100}$$

Tangohia te 1 i te 3, ka 2.

$$\frac{28}{25}=\beta \times \frac{2}{25}+\frac{4}{100}$$

Whakahekea te hautanga \frac{4}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{28}{25}=\beta \times \frac{2}{25}+\frac{1}{25}$$

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

$$\beta \times \frac{2}{25}+\frac{1}{25}=\frac{28}{25}$$

Tangohia te \frac{1}{25} mai i ngā taha e rua.

$$\beta \times \frac{2}{25}=\frac{28}{25}-\frac{1}{25}$$

Tā te mea he rite te tauraro o \frac{28}{25} me \frac{1}{25}, me tango rāua mā te tango i ō raua taurunga.

$$\beta \times \frac{2}{25}=\frac{28-1}{25}$$

Tangohia te 1 i te 28, ka 27.

$$\beta \times \frac{2}{25}=\frac{27}{25}$$

Me whakarea ngā taha e rua ki te \frac{25}{2}, te tau utu o \frac{2}{25}.

$$\beta =\frac{27}{25}\times \frac{25}{2}$$

Me whakarea te \frac{27}{25} ki te \frac{25}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\beta =\frac{27\times 25}{25\times 2}$$

Me whakakore tahi te 25 i te taurunga me te tauraro.

$$\beta =\frac{27}{2}$$