Solve 278=c/100-c578/0.2295

$$278 = \frac{ c }{ 100-c } \frac{ 578 }{ 0.2295 }$$

Solve for c

$$c = \frac{375300}{37753} = 9\frac{35523}{37753} \approx 9.940931846$$

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.

$$278\left(-c+100\right)=c\times \frac{578}{0.2295}$$

Use the distributive property to multiply 278 by -c+100.

$$-278c+27800=c\times \frac{578}{0.2295}$$

Expand \frac{578}{0.2295} by multiplying both numerator and the denominator by 10000.

$$-278c+27800=c\times \frac{5780000}{2295}$$

Reduce the fraction \frac{5780000}{2295} to lowest terms by extracting and canceling out 85.

$$-278c+27800=c\times \frac{68000}{27}$$

Subtract c\times \frac{68000}{27} from both sides.

$$-278c+27800-c\times \frac{68000}{27}=0$$

Combine -278c and -c\times \frac{68000}{27} to get -\frac{75506}{27}c.

$$-\frac{75506}{27}c+27800=0$$

Subtract 27800 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{75506}{27}c=-27800$$

Multiply both sides by -\frac{27}{75506}, the reciprocal of -\frac{75506}{27}.

$$c=-27800\left(-\frac{27}{75506}\right)$$

Multiply -27800 and -\frac{27}{75506} to get \frac{375300}{37753}.

$$c=\frac{375300}{37753}$$