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Math Help - 8th grade word problem

  1. #1
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    8th grade word problem

    My son came home with this math problem and while I have a clue to day to day math it has been 100 years since I have been in a class room. Can you help please?


    Mrs. Freeman invested a fourth of her money in stocks, a fifth in a frozen yogurt store, and a sixth in her child's college fund. She put the remaining $32,000 in the bank. What is the total amount she has invested or saved.

    Thanks for looking
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  2. #2
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    Re: 8th grade word problem

    Mrs. Freeman invested a fourth of her money in stocks, a fifth in a frozen yogurt store, and a sixth in her child's college fund. She put the remaining $32,000 in the bank. What is the total amount she has invested or saved.

    She has invested or saved all of the money in this question.
    so
    \dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6} will be the fraction not in the bank.

    The fraction IN the bank will be (1 - the fraction not in the bank)

    Now (the fraction in the bank) \times (the total) = 32000

    Let the total be y and solve the equation.

    Does that help you be less lost or do you need more help?
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  3. #3
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    Re: 8th grade word problem

    Start by giving what you want to find a "name". The problem asks "What is the total amount she has invested or saved" so let X be the total amount invested or saved.

    "Mrs. Freeman invested a fourth of her money in stocks". So she invested X/4 in stocks.
    " a fifth in a frozen yogurt store". So she invested X/5 in the store.
    "and a sixth in her child's college fund". So she put X/6 in the college fund.
    "She put the remaining $32,000 in the bank". So the total is X/4+ X/5+ X/6+ 32000= X

    X- (1/4+ 1/5+ 1/6)X= 32000.
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  4. #4
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    Re: 8th grade word problem

    Lost is no longer the word for it. LOL...

    this is how I tried it..

    solve for X

    1/4 + 1/5 + 1/6 +32000 = X

    so I would think X = 61% of the needed number
    So..

    61/100 + 32000 = X

    without X I cannot find the 61%

    or is that as far as it can go?
    Last edited by LostParent; November 20th 2013 at 03:29 PM.
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    Re: 8th grade word problem

    \frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{37}{60} ( from your calculator)

    1-\frac{37}{60}=\frac{23}{60}

    let Y be the total of all saved and invested money

    \frac{23}{60}\times Y=32000 (Remember that with fractions multiply means 'of', that is, 23/60 of Y = 32000)

    multiply both sides by \frac{60}{23}

    and you end up with

    Y=32000\times\frac{60}{23}
    Last edited by Melody2; November 20th 2013 at 04:11 PM.
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  6. #6
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    Re: 8th grade word problem

    Y = 19,733.33? so the total she started with was 51,733.33? if so thank you so much... if not, please knock some sense into my head.
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    Re: 8th grade word problem

    Quote Originally Posted by Melody2 View Post
    Y=32000\times\frac{60}{23}
    No sorry you are still not there.

    Y = 32000 times 60 divided by 23
    Get the value of Y and that is the final answer.



    Besides
    23/60 of the total is $32000

    A half would be 30/60.
    so 32000 is less than half of what you want.
    So your answer has to be more than 2 times 32000 which is $64000
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  8. #8
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    Re: 8th grade word problem

    I am sorry I am making such a big issue over such a simple problem (for you anyway) but I need to be able to explain it to my son (who WILL start taking notes in class after this), because I need to make sure he understands this.

    I follow you to 37/60. I do not however understand why you turned it around. Taking 37/60 from the whole to get 23/60. Isnt the 37/60 the number we need and 23/60 the one we have? I can 'see' that it works out as one would expect, but I do not understand why.

    I now get 51,478.26 as the invested/saved amount. (unless she deposited the 32,000 into a savings account )

    I am much to old for this.

    By the way, thank you very much for your time and effort helping us here. I do not remember much from my school days let alone something like this I would never have used again.
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  9. #9
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    Re: 8th grade word problem

    Let A = the amount of money she has saved (i.e., the answer).

    If she invested "a fourth of her money in stocks", she invested (1/4) x A, which equals (A/4).
    If she invested "a fifth in a frozen yogurt store", she invested (1/5) x A, which equals (A/5)
    If she invested "a sixth in her child's college fund", she invested (1/6) x A, which equals (A/6)
    We're then told that she put her remaining money, $32,000, into the bank.

    We know that if we add all these values, we get the amount of money she has saved, i.e., A.

    Therefore, the total amount of money she has saved can be represented by the equation (A/4) + (A/5) + (A/6) + 32000 = A
    If factor out A from the fractions, we can write this as A((1/4) + (1/5) + (1/6)) + 32000 = A
    We know that (1/4) + (1/5) + (1/6) = (37/60), and can therefore deduce that A(37/60) + 32000 = A

    That equation can be rewritten as: A - (37A/60) = 32000
    We know that "A" on its own can be written as (60A/60), and 32000 as (1920000/60). (Expressing each term with a common denominator of 60.)
    Therefore, the equation can be rewritten as (60A/60) - (37A/60) = (1920000/60)
    The denominators cancel out, leaving us with 60A - 37A = 1920000
    60A - 37A leaves us with 23A, giving us 23A = 1920000.
    If we divide both sides by 23, we get A = 1920000/23, which equals $83478.26.

    ---------------------------------------------------------------------------------------------------

    What Melody is saying is that if you have 37/60 of the money not in the bank, then you must have (60/60) - (37/60) = (23/60) in the bank. (NB: 1 is the same as (60/60).)
    So, if we think about this in percentages, she has ~38% of her money in the bank. We know that she has 38% of A (A being the total amount of money) in the bank, which we know totals $32,000. We can represent this mathematically with the equation (23/60) x A = 32000, which can be more simply written as (23A/60) = 32000.
    If we multiply both sides by 60, we get 23A = 1920000. We can then repeat the same step from the previous method and divide by 23 to get us our answer of $83478.26.
    Melody is simplifying the last step by, instead of completing both of the steps we did, shortening the process down to one step by multiplying by the reciprocal of the fraction. (If you think about what we did, you will see how this works.)

    I hope this clears things up for you (and isn't overtly incorrect). Apologies in advance for the formatting; I am yet to learn the wizardries of LaTeX.
    Last edited by Fratricide; November 20th 2013 at 09:10 PM.
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  10. #10
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    Re: 8th grade word problem

    Hi again Lost Parent,

    Please do not appologize for letting us know that you still do not understand.
    We want you to understand and we don't want you to just pretend in order to make us happy.

    Besides, speaking for myself I am using these posts to practice writing in latex, which I am not very good at yet.
    I wanted to put some dollar signs in but i haven't worked that one out yet!


    Mrs. Freeman invested a fourth of her money in stocks, a fifth in a frozen yogurt store, and a sixth in her child's college fund. She put the remaining $32,000 in the bank. What is the total amount she has invested or saved.

    \frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{37}{60}

    So the stocks plus the store plus the college fund makes up \frac{37}{60} of the entire amount that she invests or saves.

    The rest is what is in the bank.

    The whole lot has been split into 60 pieces.
    37 of those peices have been accounted for and the other (60-37) 23 pieces are in the bank.

    so \frac{23}{60} of the entire amount is in the bank. And there is $32000 in the bank.

    \frac{23}{60} \text{of the entire amount = }$32000

    Now I want the entire amount by itself so I need to get rid of the \frac{23}{60} of the left hand side.

    If I multiply the left side by \frac{60}{23} then the fraction bit will cancel out, but this is only valid if I do the same thing to the other side as well
    so

    \frac{23}{60}\times \frac{60}{23} \text{of the entire amount = } $32000\times \dfrac{60}{23}

    Now on the left hand side the 60s cancel each other out and the 23s cancel cancel each other out leaving you with 1.
    And 1 of the entire amount means 1 times the entire amount which means all of the entire amount

     \text{All of the entire amount = } \dollar 32000\times \dfrac{60}{23}

    All of the entire amount = $83478.26

    I haven't used any x's or y's I thought it might be easier for you that way.
    I hope it makes sense. But if it doesn't I will explain some more.
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  11. #11
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    Re: 8th grade word problem

    Thank you very much for all your help. Sorry I did not get back to you sooner but I wanted to make sure my son understood it completely.
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