Solve 5927/28*5514/15=AB/C

$$59 \frac { 27 } { 28 } \times 55 \frac { 14 } { 15 } = A \frac { B } { C }$$

Solve for A

$$A=\frac{1408681C}{420B}$$

$$B\neq 0\text{ and }C\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 420C, the least common multiple of 28,15,C.

$$15C\left(59\times 28+27\right)\times \frac{55\times 15+14}{15}=A\times 420B$$

Multiply 59 and 28 to get 1652.

$$15C\left(1652+27\right)\times \frac{55\times 15+14}{15}=A\times 420B$$

Add 1652 and 27 to get 1679.

$$15C\times 1679\times \frac{55\times 15+14}{15}=A\times 420B$$

Multiply 15 and 1679 to get 25185.

$$25185C\times \frac{55\times 15+14}{15}=A\times 420B$$

Multiply 55 and 15 to get 825.

$$25185C\times \frac{825+14}{15}=A\times 420B$$

Add 825 and 14 to get 839.

$$25185C\times \frac{839}{15}=A\times 420B$$

Multiply 25185 and \frac{839}{15} to get 1408681.

$$1408681C=A\times 420B$$

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

$$A\times 420B=1408681C$$

The equation is in standard form.

$$420BA=1408681C$$

Divide both sides by 420B.

$$\frac{420BA}{420B}=\frac{1408681C}{420B}$$

Dividing by 420B undoes the multiplication by 420B.

$$A=\frac{1408681C}{420B}$$

Solve for B

$$B=\frac{1408681C}{420A}$$

$$A\neq 0\text{ and }C\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 420C, the least common multiple of 28,15,C.

$$15C\left(59\times 28+27\right)\times \frac{55\times 15+14}{15}=A\times 420B$$

Multiply 59 and 28 to get 1652.

$$15C\left(1652+27\right)\times \frac{55\times 15+14}{15}=A\times 420B$$

Add 1652 and 27 to get 1679.

$$15C\times 1679\times \frac{55\times 15+14}{15}=A\times 420B$$

Multiply 15 and 1679 to get 25185.

$$25185C\times \frac{55\times 15+14}{15}=A\times 420B$$

Multiply 55 and 15 to get 825.

$$25185C\times \frac{825+14}{15}=A\times 420B$$

Add 825 and 14 to get 839.

$$25185C\times \frac{839}{15}=A\times 420B$$

Multiply 25185 and \frac{839}{15} to get 1408681.

$$1408681C=A\times 420B$$

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

$$A\times 420B=1408681C$$

The equation is in standard form.

$$420AB=1408681C$$

Divide both sides by 420A.

$$\frac{420AB}{420A}=\frac{1408681C}{420A}$$

Dividing by 420A undoes the multiplication by 420A.

$$B=\frac{1408681C}{420A}$$