Solve {l}{x+y=100}{62.5x+48.7x=50}

$$\left\{ \begin{array} { l } { x + y = 100 } \\ { 62.5 x + 48.7 x = 50 } \end{array} \right.$$

Solve for x, y

$$x=\frac{125}{278}\approx 0.449640288$$

$$y = \frac{27675}{278} = 99\frac{153}{278} \approx 99.550359712$$

Solution Steps

Consider the second equation. Combine 62.5x and 48.7x to get 111.2x.

$$111.2x=50$$

Divide both sides by 111.2.

$$x=\frac{50}{111.2}$$

Expand \frac{50}{111.2} by multiplying both numerator and the denominator by 10.

$$x=\frac{500}{1112}$$

Reduce the fraction \frac{500}{1112} to lowest terms by extracting and canceling out 4.

$$x=\frac{125}{278}$$

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

$$\frac{125}{278}+y=100$$

Subtract \frac{125}{278} from both sides.

$$y=100-\frac{125}{278}$$

Subtract \frac{125}{278} from 100 to get \frac{27675}{278}.

$$y=\frac{27675}{278}$$

The system is now solved.

$$x=\frac{125}{278} y=\frac{27675}{278}$$