2023 AMC 10B Problem 1

Problem 1 of 25EasierAlgebra

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

\frac{1}{3}

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

There’s

3 + \frac{1}{3} = \frac{10}{3}

glasses of juice in all. Split four ways, each glass ends up with

\frac{10}{3} \div 4 = \frac{5}{6}.

So a full glass has to pour out

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

Thus, C is the correct answer.

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