Solve {l}{S=100}{M=125}{P=859}{T=805}{I=S+M}{IP=c/T}{a=S/I}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { S = 100 }\\ { M = 125 }\\ { P = 859 }\\ { T = 805 }\\ { I = S + M }\\ { I P = c / T }\\ { a = S / I }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for S, M, P, T, I, c, a, b

$$b=\frac{4}{9}\approx 0.444444444$$

Solution Steps

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

$$I=100+125$$

Add 100 and 125 to get 225.

$$I=225$$

Consider the equation (6). Insert the known values of variables into the equation.

$$225\times 859=\frac{c}{805}$$

Multiply both sides of the equation by 805.

$$181125\times 859=c$$

Multiply 181125 and 859 to get 155586375.

$$155586375=c$$

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

$$c=155586375$$

Consider the equation (7). Insert the known values of variables into the equation.

$$a=\frac{100}{225}$$

Reduce the fraction \frac{100}{225} to lowest terms by extracting and canceling out 25.

$$a=\frac{4}{9}$$

Consider the equation (8). Insert the known values of variables into the equation.

$$b=\frac{4}{9}$$

The system is now solved.

$$S=100 M=125 P=859 T=805 I=225 c=155586375 a=\frac{4}{9} b=\frac{4}{9}$$