A coat's price is reduced by 15%. a) Original price 60. Calculate sale price. b) Sale price 58.14. Calculate original price.

Since the price is reduced by $15\%$, the sale price is $100\% - 15\% = 85\%$ of the original price.

$\text{Sale Price} = 0.85 \times \$60$ $\text{Sale Price} = \$51$ The sale price of the coat is \boxed{\textbf{\51}}$.

Let the original price be $P$. $0.85 \times P = \$58.14$

$P = \frac{\$58.14}{0.85}$ $P = \$68.40$ The original price of this coat is \boxed{\textbf{\68.40}}$.