John's Marble Collection

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John had a collection of marbles. He gave 1/4 of his marbles to his friend Sam and then gave 1/3 of the remaining marbles to his sister Mary. If John had 54 marbles left after giving some to Sam and Mary, how many marbles did he originally have?

Comments

  1. Rithvik2 August 2024 at 08:16

    Answer:
    John originally had 108 marbles.

    Explanation:

    Let x be the total number of marbles John originally had. John gave 1/4 of his marbles to Sam, so he had x - (1/4)x = (3/4)x marbles left. He then gave 1/3 of the remaining marbles to Mary, so he gave (1/3) × (3/4)x = (1/4)x to Mary. After giving marbles to both Sam and Mary, he had (3/4)x - (1/4)x = (2/4)x = (1/2)x marbles left. We know that John had 54 marbles left, which is (1/2)x = 54. Solving for x, we get x = 54 × 2 = 108. Therefore, John originally had 108 marbles.

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