At a school game, student tickets were sold 50 shillings each and each adult ticket were sold twice the price of each student ticket. If the total receipt from 900 tickets were 50,000 shillings, how many tickets of each kind were sold?

Acha $S$ iwe idadi ya tiketi za wanafunzi zilizouzwa.
Acha $A$ iwe idadi ya tiketi za watu wazima zilizouzwa.

Bei ya tiketi ya mwanafunzi = 50 shilingi.
Bei ya tiketi ya mtu mzima = $2 \times 50 = 100$ shilingi.

Jumla ya tiketi zilizouzwa ni 900:

$$S + A = 900 \quad \text{(Mlinganyo 1)}$$

Jumla ya mapato ni 50,000 shilingi:

$$50S + 100A = 50000 \quad \text{(Mlinganyo 2)}$$

Kutoka Mlinganyo 1, tunaweza kutoa $S$:

$$S = 900 - A$$

Badilisha $S = 900 - A$ kwenye Mlinganyo 2:

$$50(900 - A) + 100A = 50000$$

Panua mabano:

$$45000 - 50A + 100A = 50000$$

Changanya maneno ya $A$:

$$45000 + 50A = 50000$$

Toa 45000 kutoka pande zote mbili:

$$50A = 50000 - 45000$$ $$50A = 5000$$

Gawanya kwa 50:

$$A = \frac{5000}{50}$$ $$A = 100$$

Kwa hivyo, tiketi za watu wazima 100 ziliuzwa.

Badilisha $A = 100$ kwenye Mlinganyo 1 ($S = 900 - A$):

$$S = 900 - 100$$ $$S = 800$$

Kwa hivyo, tiketi za wanafunzi 800 ziliuzwa.

Jibu la mwisho ni:
Idadi ya tiketi za wanafunzi zilizouzwa: $\boxed{800}$
Idadi ya tiketi za watu wazima zilizouzwa: $\boxed{100}$