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Math Help - Inequalities help with word problem

  1. #1
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    Inequalities help with word problem

    Suppose you want to cover the back yard with decorative rock and plants and some trees. I need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rocks and trees of $2,500? Write and inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.

    Now, I can do most of this by doing basic math. I know that 30 tons of rock at 60 dollars a ton is $1800 total. I subtracted the $1800 from the $2500 and I have $700 left for trees. Trees being $84 dollars each I know that I can only by 8 trees for a total cost of $672 dollars. But I am so lost as to writing this as an inequality.

    I thought inequality symbols were greater than or less than or greater than or equal to or less than or equal to.
    I'm a bit confused as to how to write this problem as an inequality.

    Im asked if 5 would be the solution to the inequality and I know that it wont because 5 does not get me close to the 700 mark for trees.
    Im just a bit lost here.
    Last edited by n0thx; January 6th 2009 at 09:17 PM.
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  2. #2
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    Quote Originally Posted by n0thx View Post
    Suppose you want to cover the back yard with decorative rock and plants and some trees. I need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rocks and trees of $2,500? Write and inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.

    Now, I can do most of this by doing basic math. I know that 30 tons of rock at 60 dollars a ton is $1800 total. I subtracted the $1800 from the $2500 and I have $700 left for trees. Trees being $84 dollars each I know that I can only by 8 trees for a total cost of $672 dollars. But I am so lost as to writing this as an inequality.

    I thought inequality symbols were greater than or less than or greater than or equal to or less than or equal to.
    I'm a bit confused as to how to write this problem as an inequality.

    Im asked if 5 would be the solution to the inequality and I know that it wont because 5 does not get me close to the 700 mark for trees.
    Im just a bit lost here.

    Suppose max tree numbers those can buy is x, so x must be a nonnegative integer(U cann't buy or use half tree,, so inequality is


    x*84+30*60<=2500 (x is a nonnegative integer)
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  3. #3
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    Ok..so...I just want to make sure I have this correct..so I hope I say it correctly..

    The inequality is < because once the problem is solved it does not equal 2500 correct? The total amount of money used in this problem is $2472.00 making it less than $2500.00 right?

    Now to solve for the problem I need to find out what x is right?

    Then in the last part of the problem, when I am asked if 5 is a solution to the problem the answer is going to be no becuase it actually would be 8 trees that the person could buy for the the money left over from purchasing the rocks.

    Gahh...math is so hard..
    Thank you for showing me how to write it as an inequality. I feel a bit better..I just am having trouble trying to figure out when to use x as the substitution in the equation..or any equation for that matter.
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  4. #4
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    Quote Originally Posted by n0thx View Post
    Ok..so...I just want to make sure I have this correct..so I hope I say it correctly..

    The inequality is < because once the problem is solved it does not equal 2500 correct? The total amount of money used in this problem is $2472.00 making it less than $2500.00 right?

    You are all right.

    Now to solve for the problem I need to find out what x is right?

    Right.

    Then in the last part of the problem, when I am asked if 5 is a solution to the problem the answer is going to be no becuase it actually would be 8 trees that the person could buy for the the money left over from purchasing the rocks.

    Gahh...math is so hard..
    Thank you for showing me how to write it as an inequality. I feel a bit better..I just am having trouble trying to figure out when to use x as the substitution in the equation..or any equation for that matter.
    x just a meaning.
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