Azizbek Konfet
1. Muammo: Azizbekdagi konfetlar sonini topish. Ma'lum:
- Azizbekdagi konfetlarning $\frac{3}{8}$ qismi Maftunadagi konfetlarning uch baravariga teng.
- Maftunadagi konfetlar soni Azizbeknikidan 49 ta kam.
2. Belgilaymiz:
- Azizbekdagi konfetlar soni $A$
- Maftunadagi konfetlar soni $M$
3. Tenglamalarni yozamiz:
- $\frac{3}{8} A = 3M$
- $M = A - 49$
4. Birinchi tenglamani $M$ bo'yicha yechamiz:
$$\frac{3}{8} A = 3M \implies M = \frac{3}{8} \cdot \frac{A}{3} = \frac{A}{8}$$
5. Endi bu $M$ qiymatini ikkinchi tenglamaga qo'yamiz:
$$\frac{A}{8} = A - 49$$
6. Tenglamani yechamiz:
$$\frac{A}{8} - A = -49$$
$$\frac{A}{8} - \frac{8A}{8} = -49$$
$$-\frac{7A}{8} = -49$$
$$\frac{7A}{8} = 49$$
7. $A$ ni topamiz:
$$A = 49 \times \frac{8}{7} = 49 \times \frac{8}{7} = 7 \times 8 = 56$$
Javob: Azizbekdagi konfetlar soni **56** ta.