Solve (1-10%)x+(1+5%)(100-x)=100x(1+2%)

$$( 1 - 10 \% ) x + ( 1 + 5 \% ) ( 100 - x ) = 100 x ( 1 + 2 \% )$$

Solve for x

$$x = \frac{700}{681} = 1\frac{19}{681} \approx 1.027900147$$

Steps for Solving Linear Equation

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

$$\left(1-\frac{1}{10}\right)x+\left(1+\frac{5}{100}\right)\left(100-x\right)=100x\left(1+\frac{2}{100}\right)$$

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

$$\left(\frac{10}{10}-\frac{1}{10}\right)x+\left(1+\frac{5}{100}\right)\left(100-x\right)=100x\left(1+\frac{2}{100}\right)$$

Since \frac{10}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-1}{10}x+\left(1+\frac{5}{100}\right)\left(100-x\right)=100x\left(1+\frac{2}{100}\right)$$

Subtract 1 from 10 to get 9.

$$\frac{9}{10}x+\left(1+\frac{5}{100}\right)\left(100-x\right)=100x\left(1+\frac{2}{100}\right)$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{9}{10}x+\left(1+\frac{1}{20}\right)\left(100-x\right)=100x\left(1+\frac{2}{100}\right)$$

Convert 1 to fraction \frac{20}{20}.

$$\frac{9}{10}x+\left(\frac{20}{20}+\frac{1}{20}\right)\left(100-x\right)=100x\left(1+\frac{2}{100}\right)$$

Since \frac{20}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{9}{10}x+\frac{20+1}{20}\left(100-x\right)=100x\left(1+\frac{2}{100}\right)$$

Add 20 and 1 to get 21.

$$\frac{9}{10}x+\frac{21}{20}\left(100-x\right)=100x\left(1+\frac{2}{100}\right)$$

Use the distributive property to multiply \frac{21}{20} by 100-x.

$$\frac{9}{10}x+\frac{21}{20}\times 100+\frac{21}{20}\left(-1\right)x=100x\left(1+\frac{2}{100}\right)$$

Express \frac{21}{20}\times 100 as a single fraction.

$$\frac{9}{10}x+\frac{21\times 100}{20}+\frac{21}{20}\left(-1\right)x=100x\left(1+\frac{2}{100}\right)$$

Multiply 21 and 100 to get 2100.

$$\frac{9}{10}x+\frac{2100}{20}+\frac{21}{20}\left(-1\right)x=100x\left(1+\frac{2}{100}\right)$$

Divide 2100 by 20 to get 105.

$$\frac{9}{10}x+105+\frac{21}{20}\left(-1\right)x=100x\left(1+\frac{2}{100}\right)$$

Multiply \frac{21}{20} and -1 to get -\frac{21}{20}.

$$\frac{9}{10}x+105-\frac{21}{20}x=100x\left(1+\frac{2}{100}\right)$$

Combine \frac{9}{10}x and -\frac{21}{20}x to get -\frac{3}{20}x.

$$-\frac{3}{20}x+105=100x\left(1+\frac{2}{100}\right)$$

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{20}x+105=100x\left(1+\frac{1}{50}\right)$$

Convert 1 to fraction \frac{50}{50}.

$$-\frac{3}{20}x+105=100x\left(\frac{50}{50}+\frac{1}{50}\right)$$

Since \frac{50}{50} and \frac{1}{50} have the same denominator, add them by adding their numerators.

$$-\frac{3}{20}x+105=100x\times \frac{50+1}{50}$$

Add 50 and 1 to get 51.

$$-\frac{3}{20}x+105=100x\times \frac{51}{50}$$

Express 100\times \frac{51}{50} as a single fraction.

$$-\frac{3}{20}x+105=\frac{100\times 51}{50}x$$

Multiply 100 and 51 to get 5100.

$$-\frac{3}{20}x+105=\frac{5100}{50}x$$

Divide 5100 by 50 to get 102.

$$-\frac{3}{20}x+105=102x$$

Subtract 102x from both sides.

$$-\frac{3}{20}x+105-102x=0$$

Combine -\frac{3}{20}x and -102x to get -\frac{2043}{20}x.

$$-\frac{2043}{20}x+105=0$$

Subtract 105 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{2043}{20}x=-105$$

Multiply both sides by -\frac{20}{2043}, the reciprocal of -\frac{2043}{20}.

$$x=-105\left(-\frac{20}{2043}\right)$$

Express -105\left(-\frac{20}{2043}\right) as a single fraction.

$$x=\frac{-105\left(-20\right)}{2043}$$

Multiply -105 and -20 to get 2100.

$$x=\frac{2100}{2043}$$

Reduce the fraction \frac{2100}{2043} to lowest terms by extracting and canceling out 3.

$$x=\frac{700}{681}$$