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Thread: Number of Items

  1. #1
    Super Member harpazo's Avatar
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    Number of Items

    Let me try a different approach to word problems in terms of creating the right equation. I will convert (in parts) from words to algebraic language and indicate where I get stuck.

    A certain manufacturer produces items for which the production costs consist of annual fixed costs totalling 130,000 dollars and variable costs averaging 8 dollars per item.

    I understand the above to mean 130, 000 + 8x. Obviously, x must equal the number of items.

    If the manufacturer's selling price per item is 15 dollars, how many items must the manufacturer produce and sell to earn an annual profit of 150,000 dollars?

    Here is where I got stuck. It cannot be 15x + 150,000.

    Help.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Number of Items

    Profit is revenue minus costs. Assuming all items produced are sold, this gives us:

    $\displaystyle P(x)=R(x)-C(x)=(15x)-(8x+130000)=7x-130000$

    Now, to determine the number of items produced and sold to generate the given profit, we would write:

    $\displaystyle P(x)=150000$

    $\displaystyle 7x-130000=150000$

    Solving this for $\displaystyle x$ will answer the question.
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  3. #3
    Super Member harpazo's Avatar
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    Re: Number of Items

    Quote Originally Posted by MarkFL View Post
    Profit is revenue minus costs. Assuming all items produced are sold, this gives us:

    $\displaystyle P(x)=R(x)-C(x)=(15x)-(8x+130000)=7x-130000$

    Now, to determine the number of items produced and sold to generate the given profit, we would write:

    $\displaystyle P(x)=150000$

    $\displaystyle 7x-130000=150000$

    Solving this for $\displaystyle x$ will answer the question.
    7x - 130,000 = 150,000

    7x = 150,000 + 130,000

    7x = 280,000

    x = 280,000/7

    x = 40,000

    P. S. Solving the equation you provided is not the problem. My ongoing struggles with word problems have to do with creating an equation from the written words.
    Last edited by harpazo; Dec 9th 2018 at 07:54 AM.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Number of Items

    150000 + 130000 = 280000

    Thus:

    x = 40000

    If x had not been an integer, we would need to round up, since we should assume producing partial units isn't possible.
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  5. #5
    Super Member harpazo's Avatar
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    Re: Number of Items

    Quote Originally Posted by MarkFL View Post
    150000 + 130000 = 280000

    Thus:

    x = 40000

    If x had not been an integer, we would need to round up, since we should assume producing partial units isn't possible.
    I made a simple division error. Thanks.
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Number of Items

    Quote Originally Posted by harpazo View Post
    I made a simple division error. Thanks.
    The error was in your addition.
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  7. #7
    Super Member harpazo's Avatar
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    Re: Number of Items

    Quote Originally Posted by MarkFL View Post
    The error was in your addition.
    Solving math problems after working overnight is not easy. I may leave this activity for my days off. This is not an excuse. This is a reality in my life. However, I am slowly coming to the realization that creating an equation from a given application may NEVER sink in. If so, I may stop trying and focus on easier math problems, say, grades 1 to 8....
    Last edited by harpazo; Dec 9th 2018 at 10:30 PM.
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: Number of Items

    Quote Originally Posted by harpazo View Post
    Solving math problems after working overnight is not easy. I may leave this activity for my days off. This is not an excuse. This is a reality in my life. However, I am slowly coming to the realization that creating an equation from a given application may NEVER sink in. If so, I may stop trying and focus on easier math problems, say, grades 1 to 8....
    Your error was only in the addition, which I know was just a slip, not a lack of understanding of addition. Otherwise your technique for solving was correct.
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  9. #9
    Super Member harpazo's Avatar
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    Re: Number of Items

    Quote Originally Posted by MarkFL View Post
    Your error was only in the addition, which I know was just a slip, not a lack of understanding of addition. Otherwise your technique for solving was correct.
    I thank you for believing in me. I try to rationalize my way to a reasonable answer in terms of my continued struggles with converting words to algebraic language. For the life of me, I just don't get it!

    I know the basic language of algebra as the following three examples will show.

    A. The number x is twice y. This converts to x = 2y.

    B. A certain number is divided by 100. This becomes x/100.

    C. F is 3 more than a certain number. Lastly, this is F = x + 3.

    However, when it comes to GMAT, GRE and SAT applications, I am lost in space. Why is this happening? A person that finds time to practice math every given opportunity should not be struggling in this area after more than 20 years.

    You read a problem never seen before. You reason your way to the right equation. You never give up. I give up but not right away. I guess life is the way it is. Some people are very good at solving math problems and others hope to be or not to be.
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    Forum Admin topsquark's Avatar
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    Re: Number of Items

    Quote Originally Posted by harpazo View Post
    However, when it comes to GMAT, GRE and SAT applications, I am lost in space. Why is this happening? A person that finds time to practice math every given opportunity should not be struggling in this area after more than 20 years.
    I just noticed this. I don't know anything about GMAT but what the heck are you doing looking up problems on both SAT and GRE? The SAT is essentially post High School and the GRE is essentially post college. They are worlds apart in knowledge base!

    -Dan
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  11. #11
    Super Member harpazo's Avatar
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    Re: Number of Items

    Quote Originally Posted by topsquark View Post
    I just noticed this. I don't know anything about GMAT but what the heck are you doing looking up problems on both SAT and GRE? The SAT is essentially post High School and the GRE is essentially post college. They are worlds apart in knowledge base!

    -Dan
    I look up GMAT, GRE and SAT questions in terms of word problems. I have two college degrees in areas other than math. Sometimes, I look for GED and ASVAB word problems just for practice. By the way, I passed the ASVAB in 1995 and joined the Navy in April 1996.
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