what type of math is this? I am a total newbie to the world of math and was interesting in learning.  I just finished my degree(non-math) and am going to study a few math books to see if it interests me to apply for something more quantitative but I want to study something interesting with interesting problems that won't bore me.  
I thought about it, and thought of the type of problems that intrest me.  One is predicting the future and the other is predicting the past.  Here's a problem that I think would be cool. Say you have a list
calories 89, 34, 67, 43, 54, 232, 623

and someone tells you that someone had a total of "6553" calories in a day.  What type of math would try to figure this out? Is it algebra? (by the way to get this question all I did was take each value above and multiple first one by 1, second one by two, etc.up to 7.)

To cast the problem a little more clearly, you have a number of "weights", $w_1,\ldots,w_n$, in this case:
\begin{align*}
w_1 &= 89\\
w_2 &= 34\\
w_3 &= 67\\
w_4 &= 43\\
w_5 &= 54\\
w_6 &= 232\\
w_7 &= 623,
\end{align*}
and a "target total" $T$, in this case $T=6553$. You want to find nonnegative integers $a_1,\ldots,a_n$ such that
$$a_1w_1 + \cdots + a_nw_n = T.$$
In its broadest sense, this is an example of what is called a Diophantine equation (an equation in which we require the solutions to be nonnegative integers, or more generally rational numbers). They are studied in the branch of mathematics called Number theory.
