Solve 1/c_{T}=1/2+1/4+1/2+frac{1}{5}+frac{1}{3}

$$\frac { 1 } { c _ { T } } = \frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 2 } + \frac { 1 } { 5 } + \frac { 1 } { 3 }$$

Solve for c_T

$$c_{T}=\frac{60}{107}\approx 0.560747664$$

Steps for Solving Linear Equation

Variable c_{T} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 60c_{T}, the least common multiple of c_{T},2,4,5,3.

$$60=60c_{T}\times \frac{1}{2}+60c_{T}\times \frac{1}{4}+60c_{T}\times \frac{1}{2}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Multiply 60 and \frac{1}{2} to get \frac{60}{2}.

$$60=\frac{60}{2}c_{T}+60c_{T}\times \frac{1}{4}+60c_{T}\times \frac{1}{2}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Divide 60 by 2 to get 30.

$$60=30c_{T}+60c_{T}\times \frac{1}{4}+60c_{T}\times \frac{1}{2}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Multiply 60 and \frac{1}{4} to get \frac{60}{4}.

$$60=30c_{T}+\frac{60}{4}c_{T}+60c_{T}\times \frac{1}{2}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Divide 60 by 4 to get 15.

$$60=30c_{T}+15c_{T}+60c_{T}\times \frac{1}{2}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Combine 30c_{T} and 15c_{T} to get 45c_{T}.

$$60=45c_{T}+60c_{T}\times \frac{1}{2}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Multiply 60 and \frac{1}{2} to get \frac{60}{2}.

$$60=45c_{T}+\frac{60}{2}c_{T}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Divide 60 by 2 to get 30.

$$60=45c_{T}+30c_{T}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Combine 45c_{T} and 30c_{T} to get 75c_{T}.

$$60=75c_{T}+60c_{T}\times \frac{1}{5}+60c_{T}\times \frac{1}{3}$$

Multiply 60 and \frac{1}{5} to get \frac{60}{5}.

$$60=75c_{T}+\frac{60}{5}c_{T}+60c_{T}\times \frac{1}{3}$$

Divide 60 by 5 to get 12.

$$60=75c_{T}+12c_{T}+60c_{T}\times \frac{1}{3}$$

Combine 75c_{T} and 12c_{T} to get 87c_{T}.

$$60=87c_{T}+60c_{T}\times \frac{1}{3}$$

Multiply 60 and \frac{1}{3} to get \frac{60}{3}.

$$60=87c_{T}+\frac{60}{3}c_{T}$$

Divide 60 by 3 to get 20.

$$60=87c_{T}+20c_{T}$$

Combine 87c_{T} and 20c_{T} to get 107c_{T}.

$$60=107c_{T}$$

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

$$107c_{T}=60$$

Divide both sides by 107.

$$c_{T}=\frac{60}{107}$$