I was wondering what this equation I use looks like written in proper math terms

Question

I'm just going to write out the steps for an equation I use at a restaurant and I hope you in the community wouldn't mind answering by showing how the equation should be written properly.

I use this math process, or equation when dividing the quantity of cashew milk out for bottling at a restaurant I work at.
BEGIN: I have some total amount of cashew milk over 8 quarts, (though the quantity is always unknown and the equation party solves this variable part of the process). I split the total cashew milk in half for drink 1. The rest of the cashew milk goes to making 3 equal quantities of drinks 2, 3, and 4. ALTHOUGH, this half of the cashew milk is not split into 3rds because drink 4 is a coffee drink. This coffee drink is 2 parts cashew milk and 1 part coffee. Though this drink with coffee is not 100% cashew milk the end goal is to make the same quantity of this drink as I do drinks 2 and 3, which are all cashew milk by volume.
The math gets heaviest here
To figure out how much cashew milk the coffee drink (drink 4) needs I add 1 + 1 for the drinks with 100% cashew milk in them each plus 0.666 for the coffee drink which is 2/3rds cashew milk. I divide 0.666 by 2.666 and get 0.249. As a percent this rounds to 25% so I take 25% of the half of the total cashew milk. 0.333 divided by 2.666 tells me how much coffee I need. I divide 1 by 2.666 to get the percentages of drinks 2 and 3 from the total, which is 0.375 or 37.5% of the half of the total.

I hope that is clear and would just like to know if there is a proper equation form this can be written in.

Answer 1

I find this very difficult to follow here's what I understand. We have an initial volume $M$ of cashew milk. $M/2$ is set aside for drink $1$, and the remaining $M/2$ is used for drinks $2,3,4$. Drinks $2$ and $3$ take an equal volume $V$ of the milk, but drink $4$ takes $\frac23V$ so that $$V+V+\frac23V=\frac M2$$ or $$V=\frac{3M}{16}$$ The amount of coffee required $C$ is $$\frac V3=\frac{M}{16}$$

Does this answer your questions?

Answer 2

Let $V$ be the volume of milk you have to start.

Then drink $1$ uses $\frac{1}{2} V$ of the milk, and drinks $2,3,4$ together use the other $\frac{1}{2} V$.

Now let's call $C$ the volume of coffee that you will use for drink $4$. Then $2 C$ is the amount of milk used in drink $4$ (since 1/3 of the drink is coffee).

You want drinks 2,3,4 to all have the same volume (which is $3C$ by the previous discussion). So together drinks 2,3,4 have volume $9C$, of which $8C$ is milk. But we also know drinks 2,3,4 together use $\frac{1}{2} V$ of milk. So you get $$ 8C = \frac{1}{2} V $$ Which tells you $C = \frac{1}{16} V$, which in turn means $2C = \frac{1}{8}V$ is the amount of milk in the coffee drink, and $3C = \frac{3}{16}V$ is the amount of milk used for each drink 2 and 3.