Results 1 to 5 of 5

Math Help - Word problem finding an equation

  1. #1
    Senior Member
    Joined
    Feb 2008
    Posts
    297

    Word problem finding an equation

    Not too sure if this problem belongs in this section of the forum.

    A lemon tree will produce 300 lemons per year if 16 trees are planted. For every additional tree planted, the yield per tree decreases by 10 lemons per year.

    If an additional x trees are planted, show that the number of lemons produced will be:

    N=-10x^2+140x+4800
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jul 2010
    From
    Vancouver
    Posts
    432
    Thanks
    16
    What have you tried to do so far or are you completely lost?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Feb 2008
    Posts
    297
    I'm really lost:

    I know that if 16 trees are planted, that there are 300 x 16 = 4800 lemons

    But what confuses me is how they get -10x^2+140x

    I would have thought that you could just do, N = 4800 - 10(16+x)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jul 2010
    From
    Vancouver
    Posts
    432
    Thanks
    16
    You are NOT completely lost. You've got the first part right. There are indeed 4800 lemons produced when you have 16 trees. This corresponds to x = 0.

    Your mistake is in the second part. You cannot just get N = 4800 - 10(16+x) because once you plant a tree, the yield of EVERY OTHER tree decreases by 10 lemons. If x = 1, that means that you have 17 trees, each at 290 lemons per year. Once you have x = 2, you have 18 trees at 280 lemons per year. Lets see if we can make an equation out of this.

    Lets designate the number of lemons a tree makes is T(x) = 300 - 10x. That is when we plant an additional x trees, the rate of lemon production of each tree reduces by 10 lemons per year. Do you agree?

    Now that we have the rate of lemons per year, how many trees do we have? We started with 16 and we got an additional x trees. This gives us 16+x trees. Now the number of lemons produced each year is simply (16+x)T(X), which is just the number of trees multiplied by the number of lemons each tree produces. Lets multiply them out!

    \displaystyle (16+x) T(x) = (16+x)(300 - 10x) = 16.300 + 300.x - 16.10x-10x.x = 4800 +300x - 160x-10x^2 = -10x^2+140x+4800

    Is this clear? If you have any questions, ask!
    Last edited by Vlasev; August 17th 2010 at 02:26 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Jul 2010
    From
    Vancouver
    Posts
    432
    Thanks
    16
    EDIT: Double post. I don't know how this happened!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the Minimum (Word Problem)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2009, 08:28 AM
  2. Replies: 4
    Last Post: October 6th 2009, 12:11 PM
  3. Calculus Word Problem-Finding Max Profit
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 22nd 2009, 07:24 PM
  4. Replies: 2
    Last Post: March 6th 2008, 02:45 PM
  5. Finding the equation for a word problem
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: October 16th 2006, 06:04 AM

Search Tags


/mathhelpforum @mathhelpforum