Whakaoti i te Q_{1}=600-4P_{A}-0.03M-12P_{A}+15G+6P_{B}+1.5N

$$Q _ { 1 } = 600 - 4 P _ { A } - 0.03 M - 12 P _ { A } + 15 G + 6 P _ { B } + 1.5 N$$

Whakaoti mō G

$$G=\frac{M}{500}+\frac{Q_{1}}{15}+\frac{16P_{A}}{15}-\frac{N}{10}-\frac{2P_{B}}{5}-40$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pahekotia te -4P_{A} me -12P_{A}, ka -16P_{A}.

$$Q_{1}=600-16P_{A}-0.03M+15G+6P_{B}+1.5N$$

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

$$600-16P_{A}-0.03M+15G+6P_{B}+1.5N=Q_{1}$$

Tangohia te 600 mai i ngā taha e rua.

$$-16P_{A}-0.03M+15G+6P_{B}+1.5N=Q_{1}-600$$

Me tāpiri te 16P_{A} ki ngā taha e rua.

$$-0.03M+15G+6P_{B}+1.5N=Q_{1}-600+16P_{A}$$

Me tāpiri te 0.03M ki ngā taha e rua.

$$15G+6P_{B}+1.5N=Q_{1}-600+16P_{A}+0.03M$$

Tangohia te 6P_{B} mai i ngā taha e rua.

$$15G+1.5N=Q_{1}-600+16P_{A}+0.03M-6P_{B}$$

Tangohia te 1.5N mai i ngā taha e rua.

$$15G=Q_{1}-600+16P_{A}+0.03M-6P_{B}-1.5N$$

He hanga arowhānui tō te whārite.

$$15G=\frac{3M}{100}-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-600$$

Whakawehea ngā taha e rua ki te 15.

$$\frac{15G}{15}=\frac{\frac{3M}{100}-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-600}{15}$$

Mā te whakawehe ki te 15 ka wetekia te whakareanga ki te 15.

$$G=\frac{\frac{3M}{100}-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-600}{15}$$

Whakawehe Q_{1}-600+16P_{A}+\frac{3M}{100}-6P_{B}-\frac{3N}{2} ki te 15.

$$G=\frac{M}{500}+\frac{Q_{1}}{15}+\frac{16P_{A}}{15}-\frac{N}{10}-\frac{2P_{B}}{5}-40$$

Whakaoti mō M

$$M=-\frac{100Q_{1}}{3}-\frac{1600P_{A}}{3}+50N+200P_{B}+500G+20000$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pahekotia te -4P_{A} me -12P_{A}, ka -16P_{A}.

$$Q_{1}=600-16P_{A}-0.03M+15G+6P_{B}+1.5N$$

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

$$600-16P_{A}-0.03M+15G+6P_{B}+1.5N=Q_{1}$$

Tangohia te 600 mai i ngā taha e rua.

$$-16P_{A}-0.03M+15G+6P_{B}+1.5N=Q_{1}-600$$

Me tāpiri te 16P_{A} ki ngā taha e rua.

$$-0.03M+15G+6P_{B}+1.5N=Q_{1}-600+16P_{A}$$

Tangohia te 15G mai i ngā taha e rua.

$$-0.03M+6P_{B}+1.5N=Q_{1}-600+16P_{A}-15G$$

Tangohia te 6P_{B} mai i ngā taha e rua.

$$-0.03M+1.5N=Q_{1}-600+16P_{A}-15G-6P_{B}$$

Tangohia te 1.5N mai i ngā taha e rua.

$$-0.03M=Q_{1}-600+16P_{A}-15G-6P_{B}-1.5N$$

He hanga arowhānui tō te whārite.

$$-0.03M=-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-15G-600$$

Whakawehea ngā taha e rua o te whārite ki te -0.03, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-0.03M}{-0.03}=\frac{-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-15G-600}{-0.03}$$

Mā te whakawehe ki te -0.03 ka wetekia te whakareanga ki te -0.03.

$$M=\frac{-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-15G-600}{-0.03}$$

Whakawehe Q_{1}-600+16P_{A}-15G-6P_{B}-\frac{3N}{2} ki te -0.03 mā te whakarea Q_{1}-600+16P_{A}-15G-6P_{B}-\frac{3N}{2} ki te tau huripoki o -0.03.

$$M=-\frac{100Q_{1}}{3}-\frac{1600P_{A}}{3}+50N+200P_{B}+500G+20000$$