3 Equal parts plus %: I start with 30lbs of beef; customer wants 1/3 straight beef, other 2/3 w/ 40% pork ratio.

[cdalgo]

I'm sure my title is silly but here is some background to my question. I am a custom meat processor. I am constantly doing wonky math to find what seems like there would be an easy equation to figure out.

If I have 30 pounds of beef to start

customer wants 1/3 straight beef , the other 2/3 with 40% pork ratio. But I want each 1/3 to be the same after adding 40% pork ratio . Is there an equation for this?

Currently I would do 30÷3=10
Then 10÷.6=16.66

But this doesn't work really because I want to give the customer back 3 equal parts instead of 10, 16.66, and 16.66.

Is there an equation to figure out this?

 

[stapel]

I'm sure my title is silly but here is some background to my question. I am a custom meat processor. I am constantly doing wonky math to find what seems like there would be an easy equation to figure out.

If I have 30 pounds of beef to start, customer wants 1/3 straight beef , the other 2/3 with 40% pork ratio. But I want each 1/3 to be the same after adding 40% pork ratio . Is there an equation for this?

Currently I would do 30÷3=10
Then 10÷.6=16.66

But this doesn't work really because I want to give the customer back 3 equal parts instead of 10, 16.66, and 16.66.

Is there an equation to figure out this?

What do you mean, specifically, by "2/3 with 40% pork ratio"? If the customer is wanting one portion that is "straight beef" (which I'm guessing means "100% beef, with no admixture of any other sort of meat"), what do you mean when you saw that you want each of the three portions (the one that is "straight beef" and the two that are "40% pork ratio") "to be the same"?

Also, I don't understand what you are "currently" doing?

Mathematics runs on definitions, so we'll need precise information. Thank you!

 

[limiTS]

Do you mean something like this?

30 lbs of beef to start.

Split it up as:

1 of 100% beef: [imath]13.\overline{63}[/imath] lbs.

2 of 60% beef/40% pork: [imath]8.\overline{18}[/imath] lbs. of beef, each

Such that [imath]\dfrac{8.\overline{18}}{0.6}=13.\overline{63}[/imath] lbs. of beef/pork

Check: [imath]13.\overline{63}+2\cdot 8.\overline{18}=30[/imath] lbs. of beef

Then give the customer 3 equal packs of [imath]13.\overline{63}[/imath] lbs., 2 of which contain 40% pork.

 

[Dr.Peterson]

I'm sure my title is silly but here is some background to my question. I am a custom meat processor. I am constantly doing wonky math to find what seems like there would be an easy equation to figure out.

If I have 30 pounds of beef to start

customer wants 1/3 straight beef , the other 2/3 with 40% pork ratio. But I want each 1/3 to be the same after adding 40% pork ratio . Is there an equation for this?

Currently I would do 30÷3=10
Then 10÷.6=16.66

But this doesn't work really because I want to give the customer back 3 equal parts instead of 10, 16.66, and 16.66.

Is there an equation to figure out this?

Here's one way to think about it, assuming the idea is that you want the three portions to have the same weight.

Ignore the 30 pounds for the moment, and think instead about whatever amount you end up with.

Suppose you do it on a smaller scale and end up with 1 pound of pure beef, and 2 portions, each one pound, of a mixture (40% pork and 60% beef, that is, 0.4 pounds pork and 0.6 pounds beef).

Then you've used 1 + 2*0.6 = 2.2 pounds of beef.

Now we just have to scale this up to use 30 pounds of beef; which means, we multiply everything by 30/2.2 = 13.6363... . Then the first portion is 13.636 pounds of pure beef, and the other two each contain 13.636*0.4 = 5.455 pounds of pork and 13.636*0.6 = 8.182 pound of beef.

You've now used up 13.636+2*8.182 = 30 pounds of beef, and 2*5.455 = 10.91 pound of pork.

So that's one way to get @limiTS' numbers without doing any tricky math.

 

[cdalgo]

Thank yall. Yes the customer would want 40% pork added to 2/3 of the beef. I seem to have found the help need.

 

[cdalgo]

Do you mean something like this?

30 lbs of beef to start.

Split it up as:

1 of 100% beef: [imath]13.\overline{63}[/imath] lbs.

2 of 60% beef/40% pork: [imath]8.\overline{18}[/imath] lbs. of beef, each

Such that [imath]\dfrac{8.\overline{18}}{0.6}=13.\overline{63}[/imath] lbs. of beef/pork

Check: [imath]13.\overline{63}+2\cdot 8.\overline{18}=30[/imath] lbs. of beef

Then give the customer 3 equal packs of [imath]13.\overline{63}[/imath] lbs., 2 of which contain 40% pork.

Exactly like that.