AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 28 Medium

A bag contains 5 red balls, 6 white balls, and 3 black balls. In order for the probability of drawing a black ball to be \tfrac{2}{3}, how many additional black balls must be put into the bag?

  • A.

    15

  • B.

    16

  • C.

    17

  • D.

    18

  • E.

    19

Answer:E

Suppose x additional black balls need to be put into the bag. Then \frac{3+x}{5+6+3+x} = \frac{2}{3}.

Solving gives x = 19.

Therefore, 19 more black balls should be added to the bag.

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