Solve for x y=(100(0.02)+x(0.005))/(100+x)

$y = \frac{100 (0.02) + x (0.005)}{100 + x}$

Rewrite the equation as $\frac{100 (0.02) + x (0.005)}{100 + x} = y$ .

$\frac{100 (0.02) + x (0.005)}{100 + x} = y$

Factor each term.

Factor $0.000025$ out of $100 (0.02) + x (0.005)$ .

Reorder $x$ and $0.005$ .

$\frac{100 (0.02) + 0.005 x}{100 + x} = y$

Factor $0.000025$ out of $100 (0.02)$ .

$\frac{0.000025 (4000000 \cdot 0.02) + 0.005 x}{100 + x} = y$

Factor $0.000025$ out of $0.005 x$ .

$\frac{0.000025 (4000000 \cdot 0.02) + 0.000025 (200 x)}{100 + x} = y$

Factor $0.000025$ out of $0.000025 (4000000 \cdot 0.02) + 0.000025 (200 x)$ .

$\frac{0.000025 (4000000 \cdot 0.02 + 200 x)}{100 + x} = y$

Factor $4$ out of $4000000 \cdot 0.02 + 200 x$ .

Factor $4$ out of $4000000 \cdot 0.02$ .

$\frac{0.000025 (4 (1000000 \cdot 0.02) + 200 x)}{100 + x} = y$

Factor $4$ out of $200 x$ .

$\frac{0.000025 (4 (1000000 \cdot 0.02) + 4 (50 x))}{100 + x} = y$

Factor $4$ out of $4 (1000000 \cdot 0.02) + 4 (50 x)$ .

$\frac{0.000025 (4 (1000000 \cdot 0.02 + 50 x))}{100 + x} = y$

Multiply $1000000$ by $0.02$ .

$\frac{0.000025 (4 (20000 + 50 x))}{100 + x} = y$

Factor.

Factor $50$ out of $20000 + 50 x$ .

Factor $50$ out of $20000$ .

$\frac{0.000025 (4 (50 \cdot 400 + 50 x))}{100 + x} = y$

Factor $50$ out of $50 \cdot 400 + 50 x$ .

$\frac{0.000025 (4 (50 (400 + x)))}{100 + x} = y$

Remove unnecessary parentheses.

$\frac{0.000025 (4 \cdot 50 (400 + x))}{100 + x} = y$

Factor.

Multiply $4$ by $50$ .

$\frac{0.000025 (200 (400 + x))}{100 + x} = y$

Remove unnecessary parentheses.

$\frac{0.000025 \cdot 200 (400 + x)}{100 + x} = y$

Multiply $0.000025$ by $200$ .

$\frac{0.005 (400 + x)}{100 + x} = y$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$100 + x, 1$

Remove parentheses.

$100 + x, 1$

The LCM of one and any expression is the expression.

$100 + x$

Multiply each term in $\frac{0.005 (400 + x)}{100 + x} = y$ by $100 + x$ to eliminate the fractions.

Multiply each term in $\frac{0.005 (400 + x)}{100 + x} = y$ by $100 + x$ .

$\frac{0.005 (400 + x)}{100 + x} (100 + x) = y (100 + x)$

Simplify the left side.

Cancel the common factor of $0.005$ .

Cancel the common factor.

$\frac{0.005 (400 + x)}{100 + x} (100 + x) = y (100 + x)$

Rewrite the expression.

$\frac{400 + x}{100 + x} \cdot \frac{100 + x}{200} = y (100 + x)$

Cancel the common factor of $100 + x$ .

Cancel the common factor.

$\frac{400 + x}{100 + x} \cdot \frac{100 + x}{200} = y (100 + x)$

Rewrite the expression.

$(400 + x) \frac{1}{200} = y (100 + x)$

Apply the distributive property.

$400 (\frac{1}{200}) + x \frac{1}{200} = y (100 + x)$

Cancel the common factor of $200$ .

Factor $200$ out of $400$ .

$200 (2) \frac{1}{200} + x \frac{1}{200} = y (100 + x)$

Cancel the common factor.

$200 \cdot 2 \frac{1}{200} + x \frac{1}{200} = y (100 + x)$

Rewrite the expression.

$2 + x \frac{1}{200} = y (100 + x)$

Combine $x$ and $\frac{1}{200}$ .

$2 + \frac{x}{200} = y (100 + x)$

Simplify the right side.

Apply the distributive property.

$2 + \frac{x}{200} = y \cdot 100 + y x$

Move $100$ to the left of $y$ .

$2 + \frac{x}{200} = 100 y + y x$

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Subtract $y x$ from both sides of the equation.

$2 + \frac{x}{200} - y x = 100 y$

To write $- y x$ as a fraction with a common denominator, multiply by $\frac{200}{200}$ .

$2 + \frac{x}{200} - y x \cdot \frac{200}{200} = 100 y$

Combine $- y x$ and $\frac{200}{200}$ .

$2 + \frac{x}{200} + \frac{- y x \cdot 200}{200} = 100 y$

Combine the numerators over the common denominator.

$2 + \frac{x - y x \cdot 200}{200} = 100 y$

Simplify the numerator.

Factor $x$ out of $x - y x \cdot 200$ .

Raise $x$ to the power of $1$ .

$2 + \frac{x^{1} - y x \cdot 200}{200} = 100 y$

Factor $x$ out of $x^{1}$ .

$2 + \frac{x \cdot 1 - y x \cdot 200}{200} = 100 y$

Factor $x$ out of $- y x \cdot 200$ .

$2 + \frac{x \cdot 1 + x (- y \cdot 200)}{200} = 100 y$

Factor $x$ out of $x \cdot 1 + x (- y \cdot 200)$ .

$2 + \frac{x (1 - y \cdot 200)}{200} = 100 y$

Multiply $200$ by $- 1$ .

$2 + \frac{x (1 - 200 y)}{200} = 100 y$

To write $2$ as a fraction with a common denominator, multiply by $\frac{200}{200}$ .

$2 \cdot \frac{200}{200} + \frac{x (1 - 200 y)}{200} = 100 y$

Combine $2$ and $\frac{200}{200}$ .

$\frac{2 \cdot 200}{200} + \frac{x (1 - 200 y)}{200} = 100 y$

Combine the numerators over the common denominator.

$\frac{2 \cdot 200 + x (1 - 200 y)}{200} = 100 y$

Simplify the numerator.

Multiply $2$ by $200$ .

$\frac{400 + x (1 - 200 y)}{200} = 100 y$

Apply the distributive property.

$\frac{400 + x \cdot 1 + x (- 200 y)}{200} = 100 y$

Multiply $x$ by $1$ .

$\frac{400 + x + x (- 200 y)}{200} = 100 y$

Rewrite using the commutative property of multiplication.

$\frac{400 + x - 200 x y}{200} = 100 y$

Multiply both sides by $200$ .

$\frac{400 + x - 200 x y}{200} \cdot 200 = 100 y \cdot 200$

Simplify.

Simplify the left side.

Simplify $\frac{400 + x - 200 x y}{200} \cdot 200$ .

Cancel the common factor of $200$ .

Cancel the common factor.

$\frac{400 + x - 200 x y}{200} \cdot 200 = 100 y \cdot 200$

Rewrite the expression.

$400 + x - 200 x y = 100 y \cdot 200$

Simplify the expression.

Move $400$ .

$x - 200 x y + 400 = 100 y \cdot 200$

Reorder $x$ and $- 200 x y$ .

$- 200 x y + x + 400 = 100 y \cdot 200$

Simplify the right side.

Multiply $200$ by $100$ .

$- 200 x y + x + 400 = 20000 y$

Solve for $x$ .

Subtract $400$ from both sides of the equation.

$- 200 x y + x = 20000 y - 400$

Factor $x$ out of $- 200 x y + x$ .

Factor $x$ out of $- 200 x y$ .

$x (- 200 y) + x = 20000 y - 400$

Raise $x$ to the power of $1$ .

$x (- 200 y) + x = 20000 y - 400$

Factor $x$ out of $x^{1}$ .

$x (- 200 y) + x \cdot 1 = 20000 y - 400$

Factor $x$ out of $x (- 200 y) + x \cdot 1$ .

$x (- 200 y + 1) = 20000 y - 400$

Divide each term in $x (- 200 y + 1) = 20000 y - 400$ by $- 200 y + 1$ and simplify.

Divide each term in $x (- 200 y + 1) = 20000 y - 400$ by $- 200 y + 1$ .

$\frac{x (- 200 y + 1)}{- 200 y + 1} = \frac{20000 y}{- 200 y + 1} + \frac{- 400}{- 200 y + 1}$

Simplify the left side.

Cancel the common factor of $- 200 y + 1$ .

Cancel the common factor.

$\frac{x (- 200 y + 1)}{- 200 y + 1} = \frac{20000 y}{- 200 y + 1} + \frac{- 400}{- 200 y + 1}$

Divide $x$ by $1$ .

$x = \frac{20000 y}{- 200 y + 1} + \frac{- 400}{- 200 y + 1}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{20000 y - 400}{- 200 y + 1}$

Factor $400$ out of $20000 y - 400$ .

Factor $400$ out of $20000 y$ .

$x = \frac{400 (50 y) - 400}{- 200 y + 1}$

Factor $400$ out of $- 400$ .

$x = \frac{400 (50 y) + 400 (- 1)}{- 200 y + 1}$

Factor $400$ out of $400 (50 y) + 400 (- 1)$ .

$x = \frac{400 (50 y - 1)}{- 200 y + 1}$

Factor $- 1$ out of $- 200 y$ .

$x = \frac{400 (50 y - 1)}{- (200 y) + 1}$

Rewrite $1$ as $- 1 (- 1)$ .

$x = \frac{400 (50 y - 1)}{- (200 y) - 1 (- 1)}$

Factor $- 1$ out of $- (200 y) - 1 (- 1)$ .

$x = \frac{400 (50 y - 1)}{- (200 y - 1)}$

Rewrite negatives.

Rewrite $- (200 y - 1)$ as $- 1 (200 y - 1)$ .

$x = \frac{400 (50 y - 1)}{- 1 (200 y - 1)}$

Move the negative in front of the fraction.

$x = - \frac{400 (50 y - 1)}{200 y - 1}$

Solve for x y=(100(0.02)+x(0.005))/(100+x)

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