could you help me with this math problem?....please....?

Question

i'm not really good at setting up word problems...i don't need you to solve it just set up the equations in order to do so....


.....
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 grand children. 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 grand children now have an equal share, how many great grandchildren live in Georgia?

i think you have to use 'system' equations to set this up...you don't have to solve it...although it'd be appreciated...but the main thing for me is pulling out the numbers (equations) from the word problem....please help me...

Answer 1

OK - let g = the number of Georgia residents. f = the number of Floridians. Let a = the amount initially received by the Floridians - this means that the Georgians received a + 700

There are 36 grandchildren, so

g + f = 36

Each Georgian received (a + 700), each Floridian received a, and the total was 206100, so

g(a + 700) + fa = 206100

If each Georgian gave up 175, then each one kept a + 700 - 175 = a + 525. The total amount given up by the Georgians was, then, 175g. This was divided among the Floridians, so each one received 175g/f additional. We know the amounts were equal, so

a + 525 = a + 175g/f

525 = 175g/f

You have three unknowns - g, f and a. You now have three equations. Can you take it from there?

Answer 2

We need only two equations to solve the problem. The fact that the total amounts to 206,100 is not used.

g = number of ggc's in Georgia
f = number of ggc's in Florida

from the number of ggc's we have:
g + f = 36
ggc's in georgia receive an extra amount of 700 but they give 175 back => 525 remains
ggc's in Florida divide g*175 => they receive g*175/f a person

=> 525 = g*175/f
=> 525f = 175g
=> 3f = g

with g+f=36 we obtain:
3f + f = 36
=> f = 9 and g = 27

Answer 3

Alright, let's assign some variables. We'll let G be the number of great-grandchildren in Georgia and F be the number of great-grandchildren in Florida. We will also let k be the amount of money given to each great-grandchild living in florida. We start with the easy one: we have 36 great-grandchildren total, thus:

G+F = 36

Now, how much money was recieved by all the great-grandchildren living in florida? Obviously, the amount each great-grandchild recieved times the number of such grandchildren, that is k*F. The total recieved in Georgia is the number of great-grandchildren in georgia times the amount each of them recieved. How much was that? It was 700 more than a great-grandchild in florida would have recieved - that is, k+700, so the total recieved in Georgia is (k+700)G. Finally, we know that the total recieved in both places is $206,100. This gives us our second equation:

kF + (k+700)G = 206100

Finally, every grandchild in Georgia contributes $175, so after the donation the amount of money in Georgia has decreased by 175G and the amount of money in Florida has increased by the same quantity. That is, the amount of money in Florida is now kF + 175G and the amounf of money in Georgia is now (k+700)G - 175G. Dividing the amount of money in Florida by the number of grandchildren in florida gives you the amount of money each grandchild in florida now has, and likewise for the grandchildren in Georgia. But since all grandchildren now have the same amount of money, these quantities must be equal. Thus we have:
((k+700)G - 175G)/G = (kF + 175G)/F

Now we have three equations which describe the system. These are:

((k+700)G - 175G)/G = (kF + 175G)/F
kF + (k+700)G = 206100
G+F = 36

The first equation can be simplified considerably:

((k+700)G - 175G)/G = (kF + 175G)/F
k+700 - 175 = k + 175G/F
k+525 = k+175G/F
525 = 175G/F
F=175G/525
F=G/3

As you can see, this equation now contains only the variables F and G. As such, it is not necessary to invoke the second equation at all unless you want to find out how much money each child inherited. Since the problem only asks you to find the number of great-grandchildren living in Georgia, we may proceed with the substitution:

G+F = 36
G+G/3=36
4G/3=36
G=27

Answer 4

wtf