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Avg of two terms & largest possible value

  1. Dec 3, 2016 #1
    1. The problem statement, all variables and given/known data
    If the average (arithmetic mean) of 3a and 4b is less than 50, and a is twice b, what is the largest possible integer value of a?

    2. Relevant equations
    Avg of two variables is:
    (a+b)/2

    3. The attempt at a solution
    (3a + 4b)/2 < 50
    3a + 4b <100
    Now try out values such a = 2b
    I) a= 10 & b=20
    3(10) + 4(20) <100
    30 + 80 <100
    110<100 false
    2) a=9 & b = 18
    3(9) + 4(18)
    27 + 72
    99
    but this answer is not correct. Some body please guide me.
    Zulfi.
     
  2. jcsd
  3. Dec 3, 2016 #2

    Filip Larsen

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    Gold Member

    You seem to have flipped the meaning of a and b when you chose numbers.
     
  4. Dec 3, 2016 #3

    Ray Vickson

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    If you know that a = 2b, why do you not just express everything in terms of b alone?
     
  5. Dec 3, 2016 #4
  6. Dec 3, 2016 #5

    haruspex

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    2016 Award

    Yes, unless b is also supposed to be an integer. I agree it does not say so.
     
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