Solve m/49+100-98m/9/100=10%

$$\frac { \frac { m } { 49 } + \frac { 100 - 98 m } { 9 } } { 100 } = 10 \%$$

Solve for m

$$m=\frac{490}{4793}\approx 0.102232422$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 100.

$$\frac{m}{49}+\frac{100-98m}{9}=10$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 49 and 9 is 441. Multiply \frac{m}{49} times \frac{9}{9}. Multiply \frac{100-98m}{9} times \frac{49}{49}.

$$\frac{9m}{441}+\frac{49\left(100-98m\right)}{441}=10$$

Since \frac{9m}{441} and \frac{49\left(100-98m\right)}{441} have the same denominator, add them by adding their numerators.

$$\frac{9m+49\left(100-98m\right)}{441}=10$$

Do the multiplications in 9m+49\left(100-98m\right).

$$\frac{9m+4900-4802m}{441}=10$$

Combine like terms in 9m+4900-4802m.

$$\frac{-4793m+4900}{441}=10$$

Divide each term of -4793m+4900 by 441 to get -\frac{4793}{441}m+\frac{100}{9}.

$$-\frac{4793}{441}m+\frac{100}{9}=10$$

Subtract \frac{100}{9} from both sides.

$$-\frac{4793}{441}m=10-\frac{100}{9}$$

Convert 10 to fraction \frac{90}{9}.

$$-\frac{4793}{441}m=\frac{90}{9}-\frac{100}{9}$$

Since \frac{90}{9} and \frac{100}{9} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{4793}{441}m=\frac{90-100}{9}$$

Subtract 100 from 90 to get -10.

$$-\frac{4793}{441}m=-\frac{10}{9}$$

Multiply both sides by -\frac{441}{4793}, the reciprocal of -\frac{4793}{441}.

$$m=-\frac{10}{9}\left(-\frac{441}{4793}\right)$$

Multiply -\frac{10}{9} times -\frac{441}{4793} by multiplying numerator times numerator and denominator times denominator.

$$m=\frac{-10\left(-441\right)}{9\times 4793}$$

Do the multiplications in the fraction \frac{-10\left(-441\right)}{9\times 4793}.

$$m=\frac{4410}{43137}$$

Reduce the fraction \frac{4410}{43137} to lowest terms by extracting and canceling out 9.

$$m=\frac{490}{4793}$$