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Assume that x is a positive multiple of 5 and is greater than 5.

  1. Jul 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Assume that x is a positive multiple of 5 and is greater than 5. If 2x + 1 < 100, how many values for x are possible?

    2. Relevant equations



    3. The attempt at a solution


    How I solved the problem

    First manipulated inequality:

    2x+1<100
    =>
    2x < 99
    =>
    x < 49.5


    Now, x is a multiple of 5 => x = 5k for some integer k > 1 (because we are given that x > 5)

    x < 49.5 => 5k < 49.5 => k < 9.9

    So the possible values of k (since k is an integer > 1):
    2, 3, 4, 5, 6, 7, 8, 9

    So there are 6 values, namely: 5(2), 5(3), 5(4), 5(6), 5(7), 5(8), 5(9) - 10, 15, 20, 25, 30, 35, 40, 45




    Solution they have given:


    The correct answer is 17. (To gain credit for answering the question correctly you must type the number 17 in the numeric-entry box.) Given that 2x is a multiple of 5, x must be a multiple of 2.5. The total number of such multiples from 2.5 to 50 is 20. Given that x is greater than 5 and that 2x + 1 < 100, you must eliminate 2.5, 5.0, and 50 from the list of 20 multiples, which leaves 17 possible values for x.


    I am very confused by the solution they have given and have no idea what aspect of this problem I am interpreting incorrectly
     
  2. jcsd
  3. Jul 16, 2012 #2
    This seems to be the problem.
     
  4. Jul 16, 2012 #3

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi fleazo! :smile:
    clearly, there's a misprint, and the question should start "Assume that 2x is a positive multiple of 5" :wink:
     
  5. Jul 16, 2012 #4
    oh ok, thank you guys so much, I guess I should have seen that, I was just looking at it thinking, what the hell am I doing wrong
     
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