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Inequalities Word Problems

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data
    The product of two numbers is less than 340. One of the numbers is 3 less than the other. What are the possible values of the larger number?


    2. Relevant equations



    3. The attempt at a solution
    Hope this is right...

    xy < 340
    then, because y=x-3
    x(x-3) < 340
    x^2 -3x -340 < 0
    (x+17)(x-20) < 0

    Then, by using test numbers I got the interval (-17 , 20) as my solution set.

    Now, to get the larger number, do I just add 3 to every number in my possible values for y?
    Since, x=y+3 ???

    Then, possible values for x (larger number) will be (-15, 23) ?
    Or, is what I'm doing wrong
    Edit:Okay, by simple checking, 20 x 23 is larger than 340. So I guess I can't just add 3 to every y value I have. So, how do I do it? :)
    Edit:I just realized again. Since my inequality is expressed in x (larger number) doesn't that mean I got the solution set for the larger number(which is asked by problem) already?? Please correct me if I'm wrong.
    EDIT 3:So sorry for the much edits, but. In order to get the y value (I'm now asking for the smaller number), do I just minus 3 to every element in my solution set, since y is defined to be x-3 ? So, solution set for y= (-20, 17)?? Again, please correct me if I'm wrong.
    /HELP!!
     
    Last edited: Sep 16, 2012
  2. jcsd
  3. Sep 16, 2012 #2

    CAF123

    User Avatar
    Gold Member

    Yes, you are correct. Another way to find the 'smallest' numbers is to express x=y+3 and solve y(y+3)<340 to find the solution set.
     
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