Solve {l}{A+C*D=B*C}{C=4D}{D=2A}{A=120.5104}

$$\left. \begin{array} { l } { A + C \times D = B \times C } \\ { C = 4 D } \\ { D = 2 A } \\ { A = 120.5104 } \end{array} \right.$$

Solve for A, C, D, B

$$A=120.5104$$

$$C=964.0832$$

$$D=241.0208$$

$$B=241.1458$$

Solution Steps

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

$$D=2\times 120.5104$$

Multiply 2 and 120.5104 to get 241.0208.

$$D=241.0208$$

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

$$C=4\times 241.0208$$

Multiply 4 and 241.0208 to get 964.0832.

$$C=964.0832$$

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

$$120.5104+964.0832\times 241.0208=B\times 964.0832$$

Multiply 964.0832 and 241.0208 to get 232364.10413056.

$$120.5104+232364.10413056=B\times 964.0832$$

Add 120.5104 and 232364.10413056 to get 232484.61453056.

$$232484.61453056=B\times 964.0832$$

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

$$B\times 964.0832=232484.61453056$$

Divide both sides by 964.0832.

$$B=\frac{232484.61453056}{964.0832}$$

Expand \frac{232484.61453056}{964.0832} by multiplying both numerator and the denominator by 100000000.

$$B=\frac{23248461453056}{96408320000}$$

Reduce the fraction \frac{23248461453056}{96408320000} to lowest terms by extracting and canceling out 19281664.

$$B=\frac{1205729}{5000}$$

The system is now solved.

$$A=120.5104 C=964.0832 D=241.0208 B=\frac{1205729}{5000}$$