The main thing to realize here is that even though you have 15 kids, you are still only looking to find two different numbers (the amount that the 13 kids get, and the amount that the other two get). Start by assigning variables to represent these numbers.
Start by letting
D = the larger amount, that each of the 13 kids get
H = the amount each of the other 2 will get.
It doesn't matter what letters you use; I chose D for 'D'ouble, and H for 'H'alf to remind me that the the smaller amount is half of the larger amount.
Next you have to ask yourself, "What do I know about these variables?" The question tells you that the smaller amount is half the larger amount, so we can set up an equation:
H = ½ D or, equivalently, D = 2H (Can you see why these two equations are equivalent?)
Now, if you have 2 unknown variables you need two different equations in order to be able to determine what the unknowns are. (The above two equations are equivalent, so they are not different enough.) We need another equation. So, go back to the question and see what other information is given that relates the two variables:
We know that in total there is $13,826.48. So all the amounts of D dollars and H dollars must add together to get $13,826.48. Since 13 people were given $D and 2 were given $H, we have the following equation:
13D + 2H = 13826.48
and again the first equation:
D = 2H
Now you have two equations and two unknown variables. Can you take it from here?
Sue has an easier method:
If all the kids got 2 candies except for two kids who only got 1 each,
then you would have 15+13 = 28 candies in all. Now let's say that
each candy represents some particular amount of money. We will give 2
portions to 13 kids and 1 portion to each of the other 2. How big is
each portion? It is $13,826.48 split 28 ways. Divide $13,826.48 by
12 and you will find out how much to give to each of the two kids and
double it for the other thirteen kids.
Stephen La Rocque.