A girl prepared milk tea in such a way that 20% more than water. If water 12 litres only in the tea. How much tea was prepared (5 marks). 2. (x+6)/4 + (x-3-3)/5 = (5x−4)/8

Kiasi cha maji ni lita 12. Kiasi cha maziwa ni 20% zaidi ya maji.

$$\text{Kiasi cha maziwa} = \text{Kiasi cha maji} + (0.20 \times \text{Kiasi cha maji})$$ $$\text{Kiasi cha maziwa} = 12 \text{ lita} + (0.20 \times 12 \text{ lita})$$ $$\text{Kiasi cha maziwa} = 12 \text{ lita} + 2.4 \text{ lita}$$ $$\text{Kiasi cha maziwa} = 14.4 \text{ lita}$$

Jumla ya chai ni kiasi cha maji pamoja na kiasi cha maziwa.

$$\text{Jumla ya chai} = \text{Kiasi cha maji} + \text{Kiasi cha maziwa}$$ $$\text{Jumla ya chai} = 12 \text{ lita} + 14.4 \text{ lita}$$ $$\text{Jumla ya chai} = 26.4 \text{ lita}$$

Jumla ya chai iliyoandaliwa ni 26.4 lita.

$$\boxed{\text{26.4 lita}}$$

$$\frac{x-3-3}{5} = \frac{x-6}{5}$$

Mlinganyo unakuwa:

$$\frac{x+6}{4} + \frac{x-6}{5} = \frac{5x-4}{8}$$

LCM ya 4, 5, na 8 ni 40. Zidisha pande zote mbili za mlinganyo kwa 40.

$$40 \left( \frac{x+6}{4} \right) + 40 \left( \frac{x-6}{5} \right) = 40 \left( \frac{5x-4}{8} \right)$$ $$10(x+6) + 8(x-6) = 5(5x-4)$$

$$(10x + 8x) + (60 - 48) = 25x - 20$$ $$18x + 12 = 25x - 20$$

Toa $18x$ kutoka pande zote mbili:

$$12 = 25x - 18x - 20$$ $$12 = 7x - 20$$

Ongeza 20 pande zote mbili:

$$12 + 20 = 7x$$ $$32 = 7x$$

$$x = \frac{32}{7}$$

Thamani ya $x$ ni $\frac{32}{7}$.

$$\boxed{x = \frac{32}{7}}$$