Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30.

Discussion in 'Calculator Requests' started by math_celebrity, Sep 9, 2016.

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30. What is the greatest age Mary could be?

    Let e = Emily's age and m = Mary's age.

    We have the equation e = 2m + 3 and the inequality e + m < 30

    Substitute the equation for e into the inequality:
    2m + 3 + m < 30

    Add the m terms
    3m + 3 < 30

    Subtract 3 from each side of the inequality
    3m < 27

    Divide each side of the inequality by 3 to isolate m
    m < 9

    Therefore, the greatest age Mary could be is 8, since less than 9 does not include 9.
     

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