Multiple Choice Question (MCQ)

A bag contains tomatoes that are either green or red. The ratio of green tomatoes to red tomatoes in the bag is 4 to 3. When five green tomatoes and five red tomatoes are removed, the ratio becomes 3 to 2. How many red tomatoes were originally in the bag?

  1. ×

    12

  2. 15

  3. ×

    18

  4. ×

    24

  5. ×

    30

Collected in the board: Ratio

Steven Zheng posted 8 hours ago

Answer

  1. Since the ratio of green tomatoes to red tomatoes in the bag is 4 to 3, the number of green and red tomatoes can be given 4n and 3n, respectively. In this way, we can be sure that the green-to-red ratio is

    \dfrac{4n}{3n}=\dfrac{4}{3}

    If n is determined, the number of red tomatoes is determined.

    When five green tomatoes and five red tomatoes are removed, the ratio becomes 3 to 2, we can build the following equation

    \dfrac{4n-5}{3n-5} = \dfrac{3}{2}

    Cross-multiplying gives

    2(4n-5)=3(3n-5)
    8n-10=9n-15

    Then

    n = 5

    The number of red tomatoes is calculated as

    3n=15

    So B is correct

Steven Zheng posted 7 hours ago

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