#### Answer

$4\frac{1}{4} in$

#### Work Step by Step

Let x be the width of the border around the painting. The overall width of the framed painting will include the right and left borders ($2\times x$) and the 30 inch width of the painting itself.
$30+2x=38.5\longrightarrow$ subtract 30 from both sides
$30+2x-30=38.5-30\longrightarrow$ simplify
$2x=8.5\longrightarrow$ divide both sides by 2
$2x\div2=8.5\div2\longrightarrow$ simplify
$x=4.25$
Convert the decimal answer to a mixed number. Create a fraction where the number to the right of the decimal is the numerator, and the denominator is the power of 10 corresponding to the place value of the rightmost digit. Reduce the fraction to lowest terms. The number to the left of the decimal will be the whole number portion of the mixed number.
$4.2\underset\uparrow5=4\frac{25}{100}=4\frac{25\div25}{100\div25}=4\frac{1}{4}$
hundredths place