1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
    Last edited: Sep 16, 2012
  2. jcsd
  3. Sep 16, 2012 #2


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook