2023 AMC 12B Problem 1

Problem 1 of 25EasierProbability & Statistics Arithmetic

Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only

\tfrac13

full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the fourth glass so that all four glasses will have the same amount of juice?

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Solution

The total juice is

3+\tfrac13=\tfrac{10}{3}

glasses. Split evenly, each glass should hold

\tfrac{10}{3}\div 4=\tfrac{5}{6}

of a glass. Each of the first three glasses must therefore give up

1-\tfrac{5}{6}=\tfrac{1}{6}.

Thus, the correct answer is C.

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