Solve {l}{0.10=0.2{(1-S/500)}}{a=S}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { 0.10 = 0.2 {(1 - \frac{S}{500})} }\\ { a = S }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for S, a, b

$$b=250$$

Solution Steps

Consider the first equation. Divide both sides by 0.2.

$$\frac{0.1}{0.2}=1-\frac{S}{500}$$

Expand \frac{0.1}{0.2} by multiplying both numerator and the denominator by 10.

$$\frac{1}{2}=1-\frac{S}{500}$$

Multiply both sides of the equation by 500, the least common multiple of 2,500.

$$250=500-S$$

Swap sides so that all variable terms are on the left hand side.

$$500-S=250$$

Subtract 500 from both sides.

$$-S=250-500$$

Subtract 500 from 250 to get -250.

$$-S=-250$$

Divide both sides by -1.

$$S=\frac{-250}{-1}$$

Fraction \frac{-250}{-1} can be simplified to 250 by removing the negative sign from both the numerator and the denominator.

$$S=250$$

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

$$a=250$$

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

$$b=250$$

The system is now solved.

$$S=250 a=250 b=250$$