Last week, a chocolate shop sold 9 1/4 ounces of white chocolate. It sold 3 times as much milk chocolate as white chocolate. How many ounces of milk chocolate did the shop sell?

To find out how many ounces of milk chocolate the shop sold, we first need to calculate how much chocolate it sold in total.

The shop sold \( 9 \frac{1}{4} \) ounces of white chocolate. We can convert this mixed number into an improper fraction for easier calculations.

\[ 9 \frac{1}{4} = \frac{9 \times 4 + 1}{4} = \frac{36 + 1}{4} = \frac{37}{4} \]

Next, since the shop sold 3 times as much milk chocolate as white chocolate, we will multiply the amount of white chocolate by 3:

\[ \text{Milk chocolate sold} = 3 \times \left(\frac{37}{4}\right) = \frac{3 \times 37}{4} = \frac{111}{4} \]

Now, we can convert \( \frac{111}{4} \) back into a mixed number. We perform the division:

\[ 111 \div 4 = 27 \quad \text{(whole number)} \] The remainder is: \[ 111 - (4 \times 27) = 111 - 108 = 3 \] So, we have: \[ \frac{111}{4} = 27 \frac{3}{4} \]

Thus, the shop sold

\[ \boxed{27 \frac{3}{4}} \text{ ounces of milk chocolate.} \]