1. Not finding help here? Sign up for a free 30min 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!

Diophantine Equation

  1. Feb 16, 2005 #1
    The question reads:

    A farmer purchased 100 head of livestock for a total cost of $4000. Prices were as follow: calves, $120 each; lambs, $50 each; piglets, $25 each. If the farmer obtained at least one animal of each type, how many of each did he buy?

    I obtained that -240 < t < -15.789 but this can't be right as there are way too many t's to check them all. Does any one have a hint or some help?
     
  2. jcsd
  3. Feb 16, 2005 #2
    Never mind. Amazing how after looking at this problem for 4 hours, I post it here and 20 minutes later I see my mistake.
     
  4. Feb 21, 2005 #3
    This one is sort of a brute force problem, but it can be simplified. We have X+Y+Z=100, where X=calves, Y=lambs, Z=piglets. Then for the money we have:

    120X +50Y + 25Z=4000. This tells us that 5 divides X giving 5X'=X, and 2 divides Z giving 2Z' =Z. Thus form reduces to 12X' + Y+Z' = 80. Modifying the other equation gives 5X'+Y+2Z' =100. We can eliminate Y in one case, and going over the same equations eliminate Z'. Then we can look for more shortcuts or just use trial and error on the cases. Z', can not exceed 6 so there is no more than 6 cases to try.

    And be careful about looking for ALL solutions!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Diophantine Equation
  1. Diophantine equations (Replies: 1)

  2. A diophantine equation (Replies: 8)

  3. Diophantine equations (Replies: 3)

  4. Diophantine Equation (Replies: 1)

  5. Diophantine equation (Replies: 3)

Loading...