Whakaoti i te 14x*80%+(210-14x)*90%=182

$$14x \times 80 \% +(210-14x) \times 90 \% =182$$

Whakaoti mō x

$$x=5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{80}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$14x\times \frac{4}{5}+\left(210-14x\right)\times \frac{90}{100}=182$$

Tuhia te 14\times \frac{4}{5} hei hautanga kotahi.

$$\frac{14\times 4}{5}x+\left(210-14x\right)\times \frac{90}{100}=182$$

Whakareatia te 14 ki te 4, ka 56.

$$\frac{56}{5}x+\left(210-14x\right)\times \frac{90}{100}=182$$

Whakahekea te hautanga \frac{90}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$\frac{56}{5}x+\left(210-14x\right)\times \frac{9}{10}=182$$

Whakamahia te āhuatanga tohatoha hei whakarea te 210-14x ki te \frac{9}{10}.

$$\frac{56}{5}x+210\times \frac{9}{10}-14x\times \frac{9}{10}=182$$

Tuhia te 210\times \frac{9}{10} hei hautanga kotahi.

$$\frac{56}{5}x+\frac{210\times 9}{10}-14x\times \frac{9}{10}=182$$

Whakareatia te 210 ki te 9, ka 1890.

$$\frac{56}{5}x+\frac{1890}{10}-14x\times \frac{9}{10}=182$$

Whakawehea te 1890 ki te 10, kia riro ko 189.

$$\frac{56}{5}x+189-14x\times \frac{9}{10}=182$$

Tuhia te -14\times \frac{9}{10} hei hautanga kotahi.

$$\frac{56}{5}x+189+\frac{-14\times 9}{10}x=182$$

Whakareatia te -14 ki te 9, ka -126.

$$\frac{56}{5}x+189+\frac{-126}{10}x=182$$

Whakahekea te hautanga \frac{-126}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{56}{5}x+189-\frac{63}{5}x=182$$

Pahekotia te \frac{56}{5}x me -\frac{63}{5}x, ka -\frac{7}{5}x.

$$-\frac{7}{5}x+189=182$$

Tangohia te 189 mai i ngā taha e rua.

$$-\frac{7}{5}x=182-189$$

Tangohia te 189 i te 182, ka -7.

$$-\frac{7}{5}x=-7$$

Me whakarea ngā taha e rua ki te -\frac{5}{7}, te tau utu o -\frac{7}{5}.

$$x=-7\left(-\frac{5}{7}\right)$$

Whakareatia -7 ki te -\frac{5}{7}.

$$x=5$$