Solve 21%=x+(x-7.8%)*1.025

$$21 \% = x + ( x - 7.8 \% ) \times 1.025$$

Solve for x

$$x=\frac{1933}{13500}\approx 0.143185185$$

Steps for Solving Linear Equation

Expand \frac{7.8}{100} by multiplying both numerator and the denominator by 10.

$$\frac{21}{100}=x+\left(x-\frac{78}{1000}\right)\times 1.025$$

Reduce the fraction \frac{78}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{21}{100}=x+\left(x-\frac{39}{500}\right)\times 1.025$$

Use the distributive property to multiply x-\frac{39}{500} by 1.025.

$$\frac{21}{100}=x+1.025x-\frac{39}{500}\times 1.025$$

Convert decimal number 1.025 to fraction \frac{1025}{1000}. Reduce the fraction \frac{1025}{1000} to lowest terms by extracting and canceling out 25.

$$\frac{21}{100}=x+1.025x-\frac{39}{500}\times \frac{41}{40}$$

Multiply -\frac{39}{500} times \frac{41}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{100}=x+1.025x+\frac{-39\times 41}{500\times 40}$$

Do the multiplications in the fraction \frac{-39\times 41}{500\times 40}.

$$\frac{21}{100}=x+1.025x+\frac{-1599}{20000}$$

Fraction \frac{-1599}{20000} can be rewritten as -\frac{1599}{20000} by extracting the negative sign.

$$\frac{21}{100}=x+1.025x-\frac{1599}{20000}$$

Combine x and 1.025x to get 2.025x.

$$\frac{21}{100}=2.025x-\frac{1599}{20000}$$

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

$$2.025x-\frac{1599}{20000}=\frac{21}{100}$$

Add \frac{1599}{20000} to both sides.

$$2.025x=\frac{21}{100}+\frac{1599}{20000}$$

Least common multiple of 100 and 20000 is 20000. Convert \frac{21}{100} and \frac{1599}{20000} to fractions with denominator 20000.

$$2.025x=\frac{4200}{20000}+\frac{1599}{20000}$$

Since \frac{4200}{20000} and \frac{1599}{20000} have the same denominator, add them by adding their numerators.

$$2.025x=\frac{4200+1599}{20000}$$

Add 4200 and 1599 to get 5799.

$$2.025x=\frac{5799}{20000}$$

Divide both sides by 2.025.

$$x=\frac{\frac{5799}{20000}}{2.025}$$

Express \frac{\frac{5799}{20000}}{2.025} as a single fraction.

$$x=\frac{5799}{20000\times 2.025}$$

Multiply 20000 and 2.025 to get 40500.

$$x=\frac{5799}{40500}$$

Reduce the fraction \frac{5799}{40500} to lowest terms by extracting and canceling out 3.

$$x=\frac{1933}{13500}$$