2023 AMC 10B Problem 1

Question

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?

\dfrac{1}{12}

\dfrac{1}{4}

\dfrac{1}{6}

\dfrac{1}{8}

\dfrac{2}{9}

Answer: C

Concepts:fraction

Difficulty rating: 860

Small hint:

Find the total amount of juice, then divide it equally among the four glasses

Big hint:

Each full glass ends at the common level, so it must pour out

1

minus that level

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.