112%=beta(12%-4%)+4% eching

$$112 \% = \beta ( 12 \% - 4 \% ) + 4 \%$$

β uchun yechish

$$\beta =\frac{27}{2}=13,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{112}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{28}{25}=\beta \left(\frac{12}{100}-\frac{4}{100}\right)+\frac{4}{100}$$

\frac{12}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{28}{25}=\beta \left(\frac{3}{25}-\frac{4}{100}\right)+\frac{4}{100}$$

\frac{4}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{28}{25}=\beta \left(\frac{3}{25}-\frac{1}{25}\right)+\frac{4}{100}$$

\frac{3}{25} va \frac{1}{25} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{28}{25}=\beta \times \frac{3-1}{25}+\frac{4}{100}$$

2 olish uchun 3 dan 1 ni ayirish.

$$\frac{28}{25}=\beta \times \frac{2}{25}+\frac{4}{100}$$

\frac{4}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{28}{25}=\beta \times \frac{2}{25}+\frac{1}{25}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\beta \times \frac{2}{25}+\frac{1}{25}=\frac{28}{25}$$

Ikkala tarafdan \frac{1}{25} ni ayirish.

$$\beta \times \frac{2}{25}=\frac{28}{25}-\frac{1}{25}$$

\frac{28}{25} va \frac{1}{25} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\beta \times \frac{2}{25}=\frac{28-1}{25}$$

27 olish uchun 28 dan 1 ni ayirish.

$$\beta \times \frac{2}{25}=\frac{27}{25}$$

Ikki tarafini \frac{25}{2} va teskari kasri \frac{2}{25} ga ko‘paytiring.

$$\beta =\frac{27}{25}\times \frac{25}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{27}{25} ni \frac{25}{2} ga ko‘paytiring.

$$\beta =\frac{27\times 25}{25\times 2}$$

Surat va maxrajdagi ikkala 25 ni qisqartiring.

$$\beta =\frac{27}{2}$$