If (a - b)/b = 3/7, which of the following must also be true?

Discussion in 'Calculator Requests' started by math_celebrity, Aug 28, 2019.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    If (a - b)/b = 3/7, which of the following must also be true?

    A) a/b = -4/7
    B) a/b = 10/7
    C) (a + b)/b = 10/7
    D) (a - 2b)/b = -11/7

    We can rewrite (a - b)/b as:
    a/b - b/b = 3/7

    Since b/b = 1, we have:
    a/b - 1 = 3/7

    Since -1 = -7/7, we have:
    a/b - 7/7 = 3/7

    Add 7/7 to each side:
    a/b - 7/7 + 7/7 = 3/7 + 7/7

    Cancel the 7/7 on the left side, we get:
    a/b = 10/7 or Answer B

     
    Last edited: Jan 11, 2024

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