Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one yea

Discussion in 'Calculator Requests' started by math_celebrity, Dec 8, 2019.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be?

    Let my current age be a. We're given:
    4/5a > 3/4(a + 1)

    Multiply through on the right side:
    4a/5 > 3a/4 + 3/4

    Let's remove fractions by multiply through by 5:
    5(4a/5) > 5(3a/4) + 5(3/4)
    4a > 15a/4 + 15/4

    Now let's remove the other fractions by multiply through by 4:
    4(4a) > 4(15a/4) + 4(15/4)
    16a > 15a + 15

    Typing this inequality into our search engine, we get:
    a > 15

    This means the smallest integer age which the problem asks for is:
    15 + 1 = 16
     

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