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Mira, Noreen and Olivia each have 20 pretzels. After Mira gives Noreen p pretzels and Olivia gives q pretzels, the ratio of Mira's pretzels to Noreen's pretzels to Olivia's pretzels is 5:9:6. What is p + q?

  • MATH -

    Mira: 20
    Noreen: 20
    Olivia: 20
    After they give pretzels,
    M: 20 - p
    N: 20 + p + q
    O: 20 - q
    What we can do here is add all of them and equate them to the sum of the ratio multiplied by a certain factor, say x:
    (20 - p) + (20 + p + q) + (20 - q) = (5+9+6)x
    The p's and q's will all be cancelled and we're left with,
    20 + 20 + 20 = 20x
    60 = 20x
    x = 3
    Therefore, after they give their pretzels, they have
    M: 5*3 = 15
    N: 9*3 = 27
    O: 6*3 = 18
    15 = 20 - p
    p = 20 - 15
    p = 5

    18 = 20 - q
    q = 20 - 18
    q = 2

    Therefore, p + q = 7.

    Hope this helps~ :3

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