Solve (x*(1+30%)+(250-x)*(1+20%))*0.9-250=33.5

$$(x \times (1+30 \% )+(250-x) \times (1+20 \% )) \times 0.9-250=33.5$$

Solve for x

$$x=150$$

Steps for Solving Linear Equation

Reduce the fraction \frac{30}{100} to lowest terms by extracting and canceling out 10.

$$\left(x\left(1+\frac{3}{10}\right)+\left(250-x\right)\left(1+\frac{20}{100}\right)\right)\times 0.9-250=33.5$$

Convert 1 to fraction \frac{10}{10}.

$$\left(x\left(\frac{10}{10}+\frac{3}{10}\right)+\left(250-x\right)\left(1+\frac{20}{100}\right)\right)\times 0.9-250=33.5$$

Since \frac{10}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\left(x\times \frac{10+3}{10}+\left(250-x\right)\left(1+\frac{20}{100}\right)\right)\times 0.9-250=33.5$$

Add 10 and 3 to get 13.

$$\left(x\times \frac{13}{10}+\left(250-x\right)\left(1+\frac{20}{100}\right)\right)\times 0.9-250=33.5$$

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

$$\left(x\times \frac{13}{10}+\left(250-x\right)\left(1+\frac{1}{5}\right)\right)\times 0.9-250=33.5$$

Convert 1 to fraction \frac{5}{5}.

$$\left(x\times \frac{13}{10}+\left(250-x\right)\left(\frac{5}{5}+\frac{1}{5}\right)\right)\times 0.9-250=33.5$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\left(x\times \frac{13}{10}+\left(250-x\right)\times \frac{5+1}{5}\right)\times 0.9-250=33.5$$

Add 5 and 1 to get 6.

$$\left(x\times \frac{13}{10}+\left(250-x\right)\times \frac{6}{5}\right)\times 0.9-250=33.5$$

Use the distributive property to multiply 250-x by \frac{6}{5}.

$$\left(x\times \frac{13}{10}+250\times \frac{6}{5}-x\times \frac{6}{5}\right)\times 0.9-250=33.5$$

Express 250\times \frac{6}{5} as a single fraction.

$$\left(x\times \frac{13}{10}+\frac{250\times 6}{5}-x\times \frac{6}{5}\right)\times 0.9-250=33.5$$

Multiply 250 and 6 to get 1500.

$$\left(x\times \frac{13}{10}+\frac{1500}{5}-x\times \frac{6}{5}\right)\times 0.9-250=33.5$$

Divide 1500 by 5 to get 300.

$$\left(x\times \frac{13}{10}+300-x\times \frac{6}{5}\right)\times 0.9-250=33.5$$

Multiply -1 and \frac{6}{5} to get -\frac{6}{5}.

$$\left(x\times \frac{13}{10}+300-\frac{6}{5}x\right)\times 0.9-250=33.5$$

Combine x\times \frac{13}{10} and -\frac{6}{5}x to get \frac{1}{10}x.

$$\left(\frac{1}{10}x+300\right)\times 0.9-250=33.5$$

Use the distributive property to multiply \frac{1}{10}x+300 by 0.9.

$$\frac{1}{10}x\times 0.9+270-250=33.5$$

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$\frac{1}{10}x\times \frac{9}{10}+270-250=33.5$$

Multiply \frac{1}{10} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 9}{10\times 10}x+270-250=33.5$$

Do the multiplications in the fraction \frac{1\times 9}{10\times 10}.

$$\frac{9}{100}x+270-250=33.5$$

Subtract 250 from 270 to get 20.

$$\frac{9}{100}x+20=33.5$$

Subtract 20 from both sides.

$$\frac{9}{100}x=33.5-20$$

Subtract 20 from 33.5 to get 13.5.

$$\frac{9}{100}x=13.5$$

Multiply both sides by \frac{100}{9}, the reciprocal of \frac{9}{100}.

$$x=13.5\times \frac{100}{9}$$

Convert decimal number 13.5 to fraction \frac{135}{10}. Reduce the fraction \frac{135}{10} to lowest terms by extracting and canceling out 5.

$$x=\frac{27}{2}\times \frac{100}{9}$$

Multiply \frac{27}{2} times \frac{100}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{27\times 100}{2\times 9}$$

Do the multiplications in the fraction \frac{27\times 100}{2\times 9}.

$$x=\frac{2700}{18}$$

Divide 2700 by 18 to get 150.

$$x=150$$