Solve 284=(c/100-c)397/0.2295

$$284 = ( \frac { c } { 100 - c } ) \frac { 397 } { 0.2295 }$$

Solve for c

$$c = \frac{3258900}{231089} = 14\frac{23654}{231089} \approx 14.102358831$$

Steps for Solving Linear Equation

Variable c cannot be equal to 100 since division by zero is not defined. Multiply both sides of the equation by -c+100.

$$284\left(-c+100\right)=c\times \frac{397}{0.2295}$$

Use the distributive property to multiply 284 by -c+100.

$$-284c+28400=c\times \frac{397}{0.2295}$$

Expand \frac{397}{0.2295} by multiplying both numerator and the denominator by 10000.

$$-284c+28400=c\times \frac{3970000}{2295}$$

Reduce the fraction \frac{3970000}{2295} to lowest terms by extracting and canceling out 5.

$$-284c+28400=c\times \frac{794000}{459}$$

Subtract c\times \frac{794000}{459} from both sides.

$$-284c+28400-c\times \frac{794000}{459}=0$$

Combine -284c and -c\times \frac{794000}{459} to get -\frac{924356}{459}c.

$$-\frac{924356}{459}c+28400=0$$

Subtract 28400 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{924356}{459}c=-28400$$

Multiply both sides by -\frac{459}{924356}, the reciprocal of -\frac{924356}{459}.

$$c=-28400\left(-\frac{459}{924356}\right)$$

Multiply -28400 and -\frac{459}{924356} to get \frac{3258900}{231089}.

$$c=\frac{3258900}{231089}$$