AMC 8 Daily Practice Round 9

Complete problem set with solutions and individual problem pages

Problem 12 Medium

There are several boxes of cards, with each box containing the same number of cards.

- If only one box is distributed, and each child receives 8 cards, there will be a shortage of 5 cards.

- If all the boxes are distributed, each child receives 56 cards, with 8 cards remaining.

How many cards are there in each box?

  • A.

    6

  • B.

    8

  • C.

    43

  • D.

    48

  • E.

    344

Answer:C

Let there be x children. Then, the number of cards in each box is 8x - 5, and the total number of cards is 56x + 8.

Since \frac{56x + 8}{8x - 5} = \frac{43}{8x - 5} + 7

it follows that 8x - 5 must be either 1 or 43.

Solving for x, we get x = 6 (since \frac{3}{4} is discarded as it is not an integer).

Thus, the number of cards in each box is 43.

The answer is \text{C}.

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