Solve 1/9x+1/49(200-x)/200=8%

$$\frac { \frac { 1 } { 9 } x + \frac { 1 } { 49 } ( 200 - x ) } { 200 } = 8 \%$$

Solve for x

$$x = \frac{657}{5} = 131\frac{2}{5} = 131.4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 200, the least common multiple of 200,100.

$$\frac{1}{9}x+\frac{1}{49}\left(200-x\right)=2\times 8$$

Use the distributive property to multiply \frac{1}{49} by 200-x.

$$\frac{1}{9}x+\frac{1}{49}\times 200+\frac{1}{49}\left(-1\right)x=2\times 8$$

Multiply \frac{1}{49} and 200 to get \frac{200}{49}.

$$\frac{1}{9}x+\frac{200}{49}+\frac{1}{49}\left(-1\right)x=2\times 8$$

Multiply \frac{1}{49} and -1 to get -\frac{1}{49}.

$$\frac{1}{9}x+\frac{200}{49}-\frac{1}{49}x=2\times 8$$

Combine \frac{1}{9}x and -\frac{1}{49}x to get \frac{40}{441}x.

$$\frac{40}{441}x+\frac{200}{49}=2\times 8$$

Multiply 2 and 8 to get 16.

$$\frac{40}{441}x+\frac{200}{49}=16$$

Subtract \frac{200}{49} from both sides.

$$\frac{40}{441}x=16-\frac{200}{49}$$

Convert 16 to fraction \frac{784}{49}.

$$\frac{40}{441}x=\frac{784}{49}-\frac{200}{49}$$

Since \frac{784}{49} and \frac{200}{49} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40}{441}x=\frac{784-200}{49}$$

Subtract 200 from 784 to get 584.

$$\frac{40}{441}x=\frac{584}{49}$$

Multiply both sides by \frac{441}{40}, the reciprocal of \frac{40}{441}.

$$x=\frac{584}{49}\times \frac{441}{40}$$

Multiply \frac{584}{49} times \frac{441}{40} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{584\times 441}{49\times 40}$$

Do the multiplications in the fraction \frac{584\times 441}{49\times 40}.

$$x=\frac{257544}{1960}$$

Reduce the fraction \frac{257544}{1960} to lowest terms by extracting and canceling out 392.

$$x=\frac{657}{5}$$