Solve 5/32(20x/20+x+y)=6

$$\frac { 5 } { 32 } ( \frac { 20 x } { 20 + x } + y ) = 6$$

Solve for x

$$x=-\frac{20\left(5y-192\right)}{5y-92}$$

$$y\neq \frac{92}{5}$$

Steps for Solving Linear Equation

Multiply both sides by \frac{32}{5}, the reciprocal of \frac{5}{32}.

$$\frac{20x}{20+x}+y=6\times \frac{32}{5}$$

Multiply 6 and \frac{32}{5} to get \frac{192}{5}.

$$\frac{20x}{20+x}+y=\frac{192}{5}$$

Variable x cannot be equal to -20 since division by zero is not defined. Multiply both sides of the equation by 5\left(x+20\right), the least common multiple of 20+x,5.

$$5\times 20x+5\left(x+20\right)y=192\left(x+20\right)$$

Multiply 5 and 20 to get 100.

$$100x+5\left(x+20\right)y=192\left(x+20\right)$$

Use the distributive property to multiply 5 by x+20.

$$100x+\left(5x+100\right)y=192\left(x+20\right)$$

Use the distributive property to multiply 5x+100 by y.

$$100x+5xy+100y=192\left(x+20\right)$$

Use the distributive property to multiply 192 by x+20.

$$100x+5xy+100y=192x+3840$$

Subtract 192x from both sides.

$$100x+5xy+100y-192x=3840$$

Combine 100x and -192x to get -92x.

$$-92x+5xy+100y=3840$$

Subtract 100y from both sides.

$$-92x+5xy=3840-100y$$

Combine all terms containing x.

$$\left(-92+5y\right)x=3840-100y$$

The equation is in standard form.

$$\left(5y-92\right)x=3840-100y$$

Divide both sides by 5y-92.

$$\frac{\left(5y-92\right)x}{5y-92}=\frac{3840-100y}{5y-92}$$

Dividing by 5y-92 undoes the multiplication by 5y-92.

$$x=\frac{3840-100y}{5y-92}$$

Divide 3840-100y by 5y-92.

$$x=\frac{20\left(192-5y\right)}{5y-92}$$

Variable x cannot be equal to -20.

$$x=\frac{20\left(192-5y\right)}{5y-92}\text{, }x\neq -20$$

Solve for y

$$y=\frac{4\left(23x+960\right)}{5\left(x+20\right)}$$

$$x\neq -20$$

Steps for Solving Linear Equation

Multiply both sides by \frac{32}{5}, the reciprocal of \frac{5}{32}.

$$\frac{20x}{20+x}+y=6\times \frac{32}{5}$$

Multiply 6 and \frac{32}{5} to get \frac{192}{5}.

$$\frac{20x}{20+x}+y=\frac{192}{5}$$

Multiply both sides of the equation by 5\left(x+20\right), the least common multiple of 20+x,5.

$$5\times 20x+5\left(x+20\right)y=192\left(x+20\right)$$

Multiply 5 and 20 to get 100.

$$100x+5\left(x+20\right)y=192\left(x+20\right)$$

Use the distributive property to multiply 5 by x+20.

$$100x+\left(5x+100\right)y=192\left(x+20\right)$$

Use the distributive property to multiply 5x+100 by y.

$$100x+5xy+100y=192\left(x+20\right)$$

Use the distributive property to multiply 192 by x+20.

$$100x+5xy+100y=192x+3840$$

Subtract 100x from both sides.

$$5xy+100y=192x+3840-100x$$

Combine 192x and -100x to get 92x.

$$5xy+100y=92x+3840$$

Combine all terms containing y.

$$\left(5x+100\right)y=92x+3840$$

Divide both sides by 100+5x.

$$\frac{\left(5x+100\right)y}{5x+100}=\frac{92x+3840}{5x+100}$$

Dividing by 100+5x undoes the multiplication by 100+5x.

$$y=\frac{92x+3840}{5x+100}$$

Divide 92x+3840 by 100+5x.

$$y=\frac{4\left(23x+960\right)}{5\left(x+20\right)}$$