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.

Suppose you put $n$ groups of 7-apples-and-3-oranges into the big basket. Then you will have $7n$ apples and you will have $3n$ oranges in the basket.
If all of the apples are used up, you would have $7n=500$, which means you would have $n=500/7 = 71\frac37$ groups. That means you can have at most $71$ complete groups, as far as the apples are concerned.
On the other hand, if all of the oranges are used up, you would have $3n=760$, which means you would have $n=760/3=253\frac13$ groups. That means you can have at most $253$ complete groups, as far as the oranges are concerned.
So you will not be able to make any more groups once you have made $71$ groups (the apples will be exhausted then).
