Solve (120-80)*400+(120-x-80)*(500-400)/80*500=0.45

$$\frac{ (120-80) \times 400+(120-x-80) \times (500-400) }{ 80 \times 500 } =0.45$$

Solve for x

$$x=20$$

Steps for Solving Linear Equation

Subtract 80 from 120 to get 40.

$$\frac{40\times 400+\left(120-x-80\right)\left(500-400\right)}{80\times 500}=0.45$$

Multiply 40 and 400 to get 16000.

$$\frac{16000+\left(120-x-80\right)\left(500-400\right)}{80\times 500}=0.45$$

Subtract 80 from 120 to get 40.

$$\frac{16000+\left(40-x\right)\left(500-400\right)}{80\times 500}=0.45$$

Subtract 400 from 500 to get 100.

$$\frac{16000+\left(40-x\right)\times 100}{80\times 500}=0.45$$

Multiply 80 and 500 to get 40000.

$$\frac{16000+\left(40-x\right)\times 100}{40000}=0.45$$

Use the distributive property to multiply 40-x by 100.

$$\frac{16000+4000-100x}{40000}=0.45$$

Add 16000 and 4000 to get 20000.

$$\frac{20000-100x}{40000}=0.45$$

Divide each term of 20000-100x by 40000 to get \frac{1}{2}-\frac{1}{400}x.

$$\frac{1}{2}-\frac{1}{400}x=0.45$$

Subtract \frac{1}{2} from both sides.

$$-\frac{1}{400}x=0.45-\frac{1}{2}$$

Convert decimal number 0.45 to fraction \frac{45}{100}. Reduce the fraction \frac{45}{100} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{400}x=\frac{9}{20}-\frac{1}{2}$$

Least common multiple of 20 and 2 is 20. Convert \frac{9}{20} and \frac{1}{2} to fractions with denominator 20.

$$-\frac{1}{400}x=\frac{9}{20}-\frac{10}{20}$$

Since \frac{9}{20} and \frac{10}{20} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{400}x=\frac{9-10}{20}$$

Subtract 10 from 9 to get -1.

$$-\frac{1}{400}x=-\frac{1}{20}$$

Multiply both sides by -400, the reciprocal of -\frac{1}{400}.

$$x=-\frac{1}{20}\left(-400\right)$$

Express -\frac{1}{20}\left(-400\right) as a single fraction.

$$x=\frac{-\left(-400\right)}{20}$$

Multiply -1 and -400 to get 400.

$$x=\frac{400}{20}$$

Divide 400 by 20 to get 20.

$$x=20$$