2023 AMC 10B Problems/Problem 1

Solution 1

We let denote how much juice we take from each of the first children and give to the th child.

We can write the following equation: , since each value represents how much juice each child (equally) has in the end. (Each of the first three children now have juice, and hte fourth child has more juice on top of their initial .)

Solving, we see that

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