Solve {l}{A+B+C=1116}{A-1.18C=0}{A-B=60}

$$\left. \begin{array} { l } { A + B + C = 1116 } \\ { A - 1.18 C = 0 } \\ { A - B = 60 } \end{array} \right.$$

Solve for A, B, C

$$A=413$$

$$B=353$$

$$C=350$$

Short Steps Using Substitution

Solve A+B+C=1116 for A.

$$A=-B-C+1116$$

Substitute -B-C+1116 for A in the second and third equation.

$$-B-C+1116-1.18C=0 -B-C+1116-B=60$$

Solve these equations for B and C respectively.

$$B=-2.18C+1116 C=-2B+1056$$

Substitute -2.18C+1116 for B in the equation C=-2B+1056.

$$C=-2\left(-2.18C+1116\right)+1056$$

Solve C=-2\left(-2.18C+1116\right)+1056 for C.

$$C=350$$

Substitute 350 for C in the equation B=-2.18C+1116.

$$B=-2.18\times 350+1116$$

Calculate B from B=-2.18\times 350+1116.

$$B=353$$

Substitute 353 for B and 350 for C in the equation A=-B-C+1116.

$$A=-353-350+1116$$

Calculate A from A=-353-350+1116.

$$A=413$$

The system is now solved.

$$A=413 B=353 C=350$$