Solve {l}{0.75*{(x-200)}=310}{text{Solvefor}ytext{where}}{y=0.5*100+0.65*100}

$$\left. \begin{array} { l } { 0.75 \cdot {(x - 200)} = 310 }\\ { \text{Solve for } y \text{ where} } \\ { y = 0.5 \cdot 100 + 0.65 \cdot 100 } \end{array} \right.$$

Solve for x, y

$$y=115$$

Solution Steps

Consider the first equation. Divide both sides by 0.75.

$$x-200=\frac{310}{0.75}$$

Expand \frac{310}{0.75} by multiplying both numerator and the denominator by 100.

$$x-200=\frac{31000}{75}$$

Reduce the fraction \frac{31000}{75} to lowest terms by extracting and canceling out 25.

$$x-200=\frac{1240}{3}$$

Add 200 to both sides.

$$x=\frac{1240}{3}+200$$

Add \frac{1240}{3} and 200 to get \frac{1840}{3}.

$$x=\frac{1840}{3}$$

Consider the second equation. Multiply 0.5 and 100 to get 50.

$$y=50+0.65\times 100$$

Multiply 0.65 and 100 to get 65.

$$y=50+65$$

Add 50 and 65 to get 115.

$$y=115$$

The system is now solved.

$$x=\frac{1840}{3} y=115$$