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Thread: really hard word problem

  1. #1
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    really hard word problem

    Hey, I have this really tough word problem (at least I think it's tough). My math teacher found it on craigslist and thought he'd torture us with it. Here it is:

    According to Mrs. Randolph's will, each of her great-grandchildren living in Georgia received $700 more than each of her great-grandchildren living in Florida. In all, $206,100 was divided between 36 great-grandchildren. The Georgian great-grandchildren decide that the will wasn't really fair, so they each contribute $175 to be divided among the Floridian great-grandchildren. If all great-grandchildren now have an equal share, how many great-grandchildren live in Georgia?
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  2. #2
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    Hello, terrarone!

    It took me a few tries to get a grip on this one . . .


    According to Mrs. Randolph's will, each of her great-grandchildren living in GA received
    $700 more than each of her great-grandchildren living in FL. In all, $206,100 was divided
    between 36 great-grandchildren. The GA great-grandchildren decided that the will wasn't
    really fair, so they each contributed $175 to be divided among the FL great-grandchildren.
    If all great-grandchildren now have an equal share, how many great-grandchildren live in GA?

    Let $\displaystyle G$ = number of GA children.
    . . They each received $\displaystyle x$ dollars.
    They received a total of: $\displaystyle Gx$ dollars.

    Then $\displaystyle 36-G$ = number of FL children.
    . . They each received $\displaystyle x-700$ dollars.
    They received a total of: $\displaystyle (36-G)(x-700)$ dollars.

    Hence: .$\displaystyle Gx + (36-G)(x-700) \:=\:206,100 \quad\Rightarrow\quad G \:=\:\frac{231,300-36x}{700}\;\;{\color{blue}[1]}$


    The $\displaystyle G$ children from GA kicked in $175 each,
    . . so they each received: $\displaystyle x-175$ dollars.
    They received a total of: $\displaystyle G(x-175)$ dollars.

    After dividing their shares equally,
    . . the $\displaystyle (36-G)$ FL children also received: $\displaystyle x-175$ dollars each.
    They received a total of: $\displaystyle (36-G)(x-175)$ dollars.

    The grand total received was $206,100: .$\displaystyle G(x-175) + (36-G)(x-175) \;=\;206,100\;\;{\color{blue}[2]}$


    Solve [2]: .$\displaystyle Gx - 175x + 36x - 6300 - Gx + 175G \;=\;206,100$

    . . . . . $\displaystyle 36x \:=\:212,400 \quad\Rightarrow\quad x \:=\:5900$

    Substitute into [1]: . $\displaystyle G \;=\;\frac{231,300 - 36(59)}{700} \;=\;27$


    Therefore, there are 27 great-grandchldren in Georgia.

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  3. #3
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    thanks

    Wow, that's awesome! Thanks a lot!
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  4. #4
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    Answer

    700-175=525 , in order for the florida children to get 525 they need to receive three payments of 175! Which means the ratio of Georgia children to Florida children is 3 to 1! Which means there is 27 Georgia children and 9 Florida children you then add them together to get 36! Easier way. Work smarter not harder.
    Thanks from happydude3435
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