So, to understand how I noticed this let me explain a few things. I work for a tire and auto repair shop where one of my jobs main tasks is to put inventory we receive from warehouses into our computer system. This requires me to put the inventoried items into our system as measurable units that we sell them at. For example, tires are inventoried as $$1 tire, brake cleaner as $1$ can, oil as $1$ quart, and so on. This usually brings up no issues because we purchase tires at a set amount per tire and for the brake cleaner we purchase it in boxes however it is sold to us per can.
Now the oil, on the other hand, is sold to us in gallons, but we sell it as quarts. Let's say we purchased $55$ gallons of oil for $\$393.25$. What I would do is multiply the gallons by $4$ to get $220$ quarts. Then divided the $\$393.25$ by $220$ quarts to get the dollar amount of each quart. Which comes to $\$1.7875$ which obviously isn't an actual dollar amount. So at first I rounded up to $\$1.79$ and then multiplied by $220$ quarts and got $\$393.80$. Realizing that I was only a few pennies off I subtracted $393.25$ from $393.80$ and got $\$0.55$. So I reduced $55$ quarts of oil by $\$0.01$. This gave me $55$ quarts at $\$1.78$ which totals to $\$97.90$ and $165$ quarts at $\$1.79$ which totals to $\$295.35$. When these totals are added together they make $\$393.25$ are starting amount. When I looked at these numbers I noticed that there was something odd about the numbers. Which lead me to notice that the $\$1.7875$ amount I got at the start tells you right away what amount the quarts need to be separated into and at what cost to put both of them at. Basically, the first three digits ($\$\underline{1.78}75$) are going to be the cost for the first set of units and you just add $\$0.01$ to the second unit giving you $\$1.79$. The last two digits ($\$1.78\underline{75}$) tells you what percentage of your total units the second set will be, and the difference of the total units and this percentage is what your first set will be.
So here is the work:
At first, we know nothing
The $1^{st}$ set is $X$ quarts at a cost of $\$Y$ per quart and the $2^{nd}$ set is $A$ quarts at a cost of $\$B$ per quart
($\$\underline{1.78}75$) this part of the number tells you that the $1^{st}$ set's cost is $\$1.78$, and by adding $\$0.01$ to it you get $\$1.79$ for the $2^{nd}$ sets cost.
The $1^{st}$ set is $X$ quarts at a coat of $\$1.78$ per quart and the $2^{nd}$ set is $A$ quarts at a coat of $\$1.79$ per quart.
($\$1.78\underline{75}$) this part of the number tells you that the amount of quarts in the $2^{nd}$ set is $75\%$ of the $220$ quarts. By subtracting the $75\%$, which is $165$, from the $220$ quarts you get $55$ quarts for the total amount of quarts for the first set.
The $1^{st}$ set is $55$ quarts at a coat of $\$1.78$ per quart and the $2^{nd}$ set is $165$ quarts at a coat of $\$1.79$ per quart.
Is there a name or set of rules that explains this occurrence?
It's called proportionality, and you're using an implicit ratio of $0.75:0.25$ or $3:1$.
For every quart you reduce by 0.75 cents, you increase three quarts by 0.25 cents, so that all quarts have a cost which is a multiple of 1 cent.
The number of quarts with the lowered cost will be one-third of the number of quarts with the raised cost, and will be one-quarter of the original total (respectively: raised cost, lowered cost, three times, three-quarters).