Solve {l}{x+y=25000}{x/600+x/200=75}

$$\left. \begin{array} { l } { x + y = 25000 } \\ { \frac { x } { 600 } + \frac { x } { 200 } = 75 } \end{array} \right.$$

Solve for x, y

$$x=11250$$

$$y=13750$$

Solution Steps

Consider the second equation. Multiply both sides of the equation by 600, the least common multiple of 600,200.

$$x+3x=45000$$

Combine x and 3x to get 4x.

$$4x=45000$$

Divide both sides by 4.

$$x=\frac{45000}{4}$$

Divide 45000 by 4 to get 11250.

$$x=11250$$

Consider the first equation. Insert the known values of variables into the equation.

$$11250+y=25000$$

Subtract 11250 from both sides.

$$y=25000-11250$$

Subtract 11250 from 25000 to get 13750.

$$y=13750$$

The system is now solved.

$$x=11250 y=13750$$