Chapter 7 - Algebraic Fractions - 7.5 - Fractional Equations and Problem Solving - Problem Set 7.5 - Page 306: 28

$n = 52$

1. Multiply by $57-n$ on both sides of the equation to remove the fractions: $\frac{n}{57-n} = 10 + \frac{2}{57-n}$ $n= 10(57-n) + \frac{2(57-n)}{57-n}$ 2. Cancel out $57-n$ to simplify: $n= 10(57-n) + 2$ 3. Expand and solve for $n$ $n = 570 - 10n + 2$ $n - 570 + 10n - 2=0 $ $11n - 572 = 0$ $11(n-52) = 0$ $n - 52 = 0$ $n = 52$