Prepare for me age problem question so that I can solve

Kutokana na taarifa ya kwanza:

$$T = \frac{1}{3}M \quad \text{(Mlinganyo 1)}$$

Umri wa mama utakuwa $M+5$.
Umri wa mtoto utakuwa $T+5$.
Kutokana na taarifa ya pili:

$$T+5 = \frac{1}{2}(M+5) \quad \text{(Mlinganyo 2)}$$

$$\frac{1}{3}M + 5 = \frac{1}{2}M + \frac{1}{2} \times 5$$ $$\frac{1}{3}M + 5 = \frac{1}{2}M + \frac{5}{2}$$

Toa $\frac{1}{3}M$ kutoka pande zote mbili na toa $\frac{5}{2}$ kutoka pande zote mbili.

$$5 - \frac{5}{2} = \frac{1}{2}M - \frac{1}{3}M$$

Pata kigawo cha kawaida kwa namba (2) na kwa vigezo (6).

$$\frac{10}{2} - \frac{5}{2} = \frac{3}{6}M - \frac{2}{6}M$$ $$\frac{5}{2} = \frac{1}{6}M$$

$$M = \frac{5}{2} \times 6$$ $$M = 5 \times 3$$ $$M = 15$$

Jibu: Umri wa mama wa sasa ni miaka 15.