Solve {l}{x+y=29,000}{0.06x+0.15x=3090}

$$\left. \begin{array} { l } { x + y = 29,000 } \\ { 0.06 x + 0.15 x = 3090 } \end{array} \right.$$

Solve for x, y

$$x = \frac{103000}{7} = 14714\frac{2}{7} \approx 14714.285714286$$

$$y = \frac{100000}{7} = 14285\frac{5}{7} \approx 14285.714285714$$

Solution Steps

Consider the second equation. Combine 0.06x and 0.15x to get 0.21x.

$$0.21x=3090$$

Divide both sides by 0.21.

$$x=\frac{3090}{0.21}$$

Expand \frac{3090}{0.21} by multiplying both numerator and the denominator by 100.

$$x=\frac{309000}{21}$$

Reduce the fraction \frac{309000}{21} to lowest terms by extracting and canceling out 3.

$$x=\frac{103000}{7}$$

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

$$\frac{103000}{7}+y=29000$$

Subtract \frac{103000}{7} from both sides.

$$y=29000-\frac{103000}{7}$$

Subtract \frac{103000}{7} from 29000 to get \frac{100000}{7}.

$$y=\frac{100000}{7}$$

The system is now solved.

$$x=\frac{103000}{7} y=\frac{100000}{7}$$