Solve 20%*x+8%*40=12%*(x+40)

$$20 \% \times x+8 \% \times 40=12 \% \times (x+40)$$

Solve for x

$$x=20$$

Steps for Solving Linear Equation

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$\frac{1}{5}x+\frac{8}{100}\times 40=\frac{12}{100}\left(x+40\right)$$

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{1}{5}x+\frac{2}{25}\times 40=\frac{12}{100}\left(x+40\right)$$

Express \frac{2}{25}\times 40 as a single fraction.

$$\frac{1}{5}x+\frac{2\times 40}{25}=\frac{12}{100}\left(x+40\right)$$

Multiply 2 and 40 to get 80.

$$\frac{1}{5}x+\frac{80}{25}=\frac{12}{100}\left(x+40\right)$$

Reduce the fraction \frac{80}{25} to lowest terms by extracting and canceling out 5.

$$\frac{1}{5}x+\frac{16}{5}=\frac{12}{100}\left(x+40\right)$$

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

$$\frac{1}{5}x+\frac{16}{5}=\frac{3}{25}\left(x+40\right)$$

Use the distributive property to multiply \frac{3}{25} by x+40.

$$\frac{1}{5}x+\frac{16}{5}=\frac{3}{25}x+\frac{3}{25}\times 40$$

Express \frac{3}{25}\times 40 as a single fraction.

$$\frac{1}{5}x+\frac{16}{5}=\frac{3}{25}x+\frac{3\times 40}{25}$$

Multiply 3 and 40 to get 120.

$$\frac{1}{5}x+\frac{16}{5}=\frac{3}{25}x+\frac{120}{25}$$

Reduce the fraction \frac{120}{25} to lowest terms by extracting and canceling out 5.

$$\frac{1}{5}x+\frac{16}{5}=\frac{3}{25}x+\frac{24}{5}$$

Subtract \frac{3}{25}x from both sides.

$$\frac{1}{5}x+\frac{16}{5}-\frac{3}{25}x=\frac{24}{5}$$

Combine \frac{1}{5}x and -\frac{3}{25}x to get \frac{2}{25}x.

$$\frac{2}{25}x+\frac{16}{5}=\frac{24}{5}$$

Subtract \frac{16}{5} from both sides.

$$\frac{2}{25}x=\frac{24}{5}-\frac{16}{5}$$

Since \frac{24}{5} and \frac{16}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{25}x=\frac{24-16}{5}$$

Subtract 16 from 24 to get 8.

$$\frac{2}{25}x=\frac{8}{5}$$

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

$$x=\frac{8}{5}\times \frac{25}{2}$$

Multiply \frac{8}{5} times \frac{25}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{8\times 25}{5\times 2}$$

Do the multiplications in the fraction \frac{8\times 25}{5\times 2}.

$$x=\frac{200}{10}$$

Divide 200 by 10 to get 20.

$$x=20$$