Questions: Mr. Smith has an online cooking show. Before he films an episode about baking the perfect pound cake, he prepares his ingredients. His recipe calls for 2 1/2 cups of sugar for the cake and 1 1/4 cups of sugar for the vanilla glaze. How many 1/4-cup scoops of sugar does he need? Write your answer as a whole number, fraction, or mixed number. Simplify any fractions. scoops

Solution Steps

To find out how many \(\frac{1}{4}\)-cup scoops of sugar Mr. Smith needs, we first need to determine the total amount of sugar required for both the cake and the glaze. We then convert this total amount into the number of \(\frac{1}{4}\)-cup scoops. This involves adding the fractions for the sugar amounts and then dividing the total by \(\frac{1}{4}\).

To find the total amount of sugar required, we add the sugar needed for the cake and the glaze. The recipe calls for \(2 \frac{1}{2}\) cups of sugar for the cake and \(1 \frac{1}{4}\) cups for the glaze. We convert these mixed numbers to improper fractions:

\[ 2 \frac{1}{2} = \frac{5}{2}, \quad 1 \frac{1}{4} = \frac{5}{4} \]

Adding these fractions gives:

\[ \frac{5}{2} + \frac{5}{4} = \frac{10}{4} + \frac{5}{4} = \frac{15}{4} \]

Thus, the total amount of sugar needed is \(\frac{15}{4}\) cups.

To find out how many \(\frac{1}{4}\)-cup scoops are needed, we divide the total amount of sugar by \(\frac{1}{4}\):

\[ \frac{15}{4} \div \frac{1}{4} = \frac{15}{4} \times \frac{4}{1} = 15 \]

Final Answer