Solve 60%text{of}(x-y)=40%(x+y)

$$60 \% \text { of } ( x - y ) = 40 \% ( x + y )$$

Solve for x

$$x=5y$$

Steps for Solving Linear Equation

Reduce the fraction \frac{60}{100} to lowest terms by extracting and canceling out 20.

$$\frac{3}{5}\left(x-y\right)=\frac{40}{100}\left(x+y\right)$$

Use the distributive property to multiply \frac{3}{5} by x-y.

$$\frac{3}{5}x-\frac{3}{5}y=\frac{40}{100}\left(x+y\right)$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$\frac{3}{5}x-\frac{3}{5}y=\frac{2}{5}\left(x+y\right)$$

Use the distributive property to multiply \frac{2}{5} by x+y.

$$\frac{3}{5}x-\frac{3}{5}y=\frac{2}{5}x+\frac{2}{5}y$$

Subtract \frac{2}{5}x from both sides.

$$\frac{3}{5}x-\frac{3}{5}y-\frac{2}{5}x=\frac{2}{5}y$$

Combine \frac{3}{5}x and -\frac{2}{5}x to get \frac{1}{5}x.

$$\frac{1}{5}x-\frac{3}{5}y=\frac{2}{5}y$$

Add \frac{3}{5}y to both sides.

$$\frac{1}{5}x=\frac{2}{5}y+\frac{3}{5}y$$

Combine \frac{2}{5}y and \frac{3}{5}y to get y.

$$\frac{1}{5}x=y$$

Multiply both sides by 5.

$$\frac{\frac{1}{5}x}{\frac{1}{5}}=\frac{y}{\frac{1}{5}}$$

Dividing by \frac{1}{5} undoes the multiplication by \frac{1}{5}.

$$x=\frac{y}{\frac{1}{5}}$$

Divide y by \frac{1}{5} by multiplying y by the reciprocal of \frac{1}{5}.

$$x=5y$$

Solve for y

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

Steps for Solving Linear Equation

Reduce the fraction \frac{60}{100} to lowest terms by extracting and canceling out 20.

$$\frac{3}{5}\left(x-y\right)=\frac{40}{100}\left(x+y\right)$$

Use the distributive property to multiply \frac{3}{5} by x-y.

$$\frac{3}{5}x-\frac{3}{5}y=\frac{40}{100}\left(x+y\right)$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$\frac{3}{5}x-\frac{3}{5}y=\frac{2}{5}\left(x+y\right)$$

Use the distributive property to multiply \frac{2}{5} by x+y.

$$\frac{3}{5}x-\frac{3}{5}y=\frac{2}{5}x+\frac{2}{5}y$$

Subtract \frac{2}{5}y from both sides.

$$\frac{3}{5}x-\frac{3}{5}y-\frac{2}{5}y=\frac{2}{5}x$$

Combine -\frac{3}{5}y and -\frac{2}{5}y to get -y.

$$\frac{3}{5}x-y=\frac{2}{5}x$$

Subtract \frac{3}{5}x from both sides.

$$-y=\frac{2}{5}x-\frac{3}{5}x$$

Combine \frac{2}{5}x and -\frac{3}{5}x to get -\frac{1}{5}x.

$$-y=-\frac{1}{5}x$$

The equation is in standard form.

$$-y=-\frac{x}{5}$$

Divide both sides by -1.

$$\frac{-y}{-1}=-\frac{\frac{x}{5}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=-\frac{\frac{x}{5}}{-1}$$

Divide -\frac{x}{5} by -1.

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