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

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

Solve for β

$$\beta =\frac{27}{2}=13.5$$

Steps for Solving Linear Equation

Reduce the fraction \frac{112}{100} to lowest terms by extracting and canceling out 4.

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

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

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

Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

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

Since \frac{3}{25} and \frac{1}{25} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 3 to get 2.

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

Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract \frac{1}{25} from both sides.

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

Since \frac{28}{25} and \frac{1}{25} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 28 to get 27.

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

Multiply both sides by \frac{25}{2}, the reciprocal of \frac{2}{25}.

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

Multiply \frac{27}{25} times \frac{25}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 25 in both numerator and denominator.

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