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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 2122 \frac{1}{2} cups of sugar for the cake and 1141 \frac{1}{4} cups of sugar for the vanilla glaze. How many 14\frac{1}{4}-cup scoops of sugar does he need? \newlineWrite your answer as a whole number, fractions" target="_blank" class="backlink">fraction, or mixed number. Simplify any fractions.\newline____ scoops

Full solution

Q. 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 2122 \frac{1}{2} cups of sugar for the cake and 1141 \frac{1}{4} cups of sugar for the vanilla glaze. How many 14\frac{1}{4}-cup scoops of sugar does he need? \newlineWrite your answer as a whole number, fraction, or mixed number. Simplify any fractions.\newline____ scoops
  1. Convert to Improper Fractions: Convert mixed numbers to improper fractions for easier calculation. 2122 \frac{1}{2} cups of sugar becomes 52\frac{5}{2} cups, and 1141 \frac{1}{4} cups becomes 54\frac{5}{4} cups.
  2. Add Amounts Together: Add the two amounts of sugar together. 52+54=(104)+(54)=154\frac{5}{2} + \frac{5}{4} = \left(\frac{10}{4}\right) + \left(\frac{5}{4}\right) = \frac{15}{4} cups of sugar in total.
  3. Convert to Scoops: Convert total cups of sugar to 14\frac{1}{4}-cup scoops. Since 11 cup = 44 scoops of 14\frac{1}{4} cup, then 154\frac{15}{4} cups = (154)×4=15\left(\frac{15}{4}\right) \times 4 = 15 scoops.

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