How to adjust a ratio to create desired proportion Let's say I have a bunch of apples and oranges. Specifically 500 apples and 760 oranges. 
I need to create a big basket of fruit. For every 7 apples I include, I need to include 3 oranges. 
I want to make the biggest basket possible using as much of my fruit as I can while honoring the desired apple to orange ratio.
I'm not mathematically inclined and I've been just taking bunches of 7 and 3 at a time until I run out. There has to be some kind of formula I can use to tell me upfront the max number of each that I should pull.
Thanks in advance.

You have more oranges than apples at your disposal, but you need more than twice as many apples in the basket as you do oranges.
So, you'll run out of apples and have a lot of oranges left over.
If you have $7$ apples, you need $3$ oranges.
If you have $14$ apples, you need $6$ oranges.
If you have $7n$ apples, where $n$ is a positive integer, then you'll need $3n$ oranges.
What value of $n$ will let you use most of the apples?  Well, we can calculate
$$7n = 500 \to n = 71\text{ }3/7.$$
So $n = 71$, which means the number of apples is $7n = 7 \cdot 71 = 497$ and the number of oranges is $3n = 3 \cdot 71 = 213.$
