# Math Help - really hard word problem

1. ## 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? 2. 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 $G$ = number of GA children.
. . They each received $x$ dollars.
They received a total of: $Gx$ dollars.

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

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

The $G$ children from GA kicked in $175 each, . . so they each received: $x-175$ dollars. They received a total of: $G(x-175)$ dollars. After dividing their shares equally, . . the $(36-G)$ FL children also received: $x-175$ dollars each. They received a total of: $(36-G)(x-175)$ dollars. The grand total received was$206,100: . $G(x-175) + (36-G)(x-175) \;=\;206,100\;\;{\color{blue}[2]}$

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

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

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

Therefore, there are 27 great-grandchldren in Georgia.

3. ## thanks

Wow, that's awesome! Thanks a lot!