Algebra problem with two variables

[tbmac61]

Hi, I'm a new member and working on a project at work and not coming up with an answer.
We mix two products together with different known densities.
An example is the 2 individual ingredient densities are 48 and 70.
After they are mixed the known total density equals an example of 52.
My question is:
I need a formula to figure out how many pounds of each density material do I need to get to the total mixed density of 52.
The total pounds of both ingredients must equal 2000 lbs.
I have the answer by way of trial and error.
The answer is 1636 lbs of 48 lb material and 364 lbs of 70 lb material.
This gives me
1636x48=78528
364x70=25480
The 1636 + 364 = 2000 (constant)
Add 78528 + 25480 = 104008 /2000 = 52.004 total density
I need a formula where the (2) individual and mixed densities are known and the 2000 lb limit is constant and will tell me the ingredient totals.
Thank you very much for any help you can provide!

[Ace_XL]

Like this..

[tbmac61]

Thank you Ace_XL so much.
Exactly what I needed!

[vamosj]

Ace, if you play around with that one, the final density doesn't = 52.

I changed the density of Material A and came out with a density of 58 as per OP's calculations in his post.

[daffodil11]

(48x+70x)÷2000 = 52

118x = 104000

x = 881.3559

(48 density x 881.3559 lbs) + (70 density x 881.3559 lbs) = 104,000 lbs ÷ 2000 = 52 density


With the limited information, there's technically an infinite number of solutions; mine only shows an equal parts solution.

The missing variable is volume. If we knew the capacity, we could nail down something a little more concrete.

[vamosj]

(48x+70x)÷2000 = 52

118x = 104000

x = 881.3559

(48 density x 881.3559 lbs) + (70 density x 881.3559 lbs) = 104,000 lbs ÷ 2000 = 52 density


With the limited information, there's technically an infinite number of solutions; mine only shows an equal parts solution.

The missing variable is volume. If we knew the capacity, we could nail down something a little more concrete.

Yeah, but that's the problem he's encountering... He's given two materials, of which he knows the density of the item but not the volume... I think this might best be figured out with a macro to do the "Easter Egg" work for him.

[tbmac61]

(48x+70x)÷2000 = 52

118x = 104000

x = 881.3559

(48 density x 881.3559 lbs) + (70 density x 881.3559 lbs) = 104,000 lbs ÷ 2000 = 52 density


With the limited information, there's technically an infinite number of solutions; mine only shows an equal parts solution.

The missing variable is volume. If we knew the capacity, we could nail down something a little more concrete.

Both densities can't be 881.3559, the two added together must total 2000 lbs

[daffodil11]

Well gosh. I just re-read the OP and things are making a lot more sense.

Ace's proportionality works great.

[vamosj]

I need a formula where the (2) individual and mixed densities are known and the 2000 lb limit is constant and will tell me the ingredient totals.
Thank you very much for any help you can provide!

I was reading this part as the material density may change, but he knows the density of the item he'll be mixing..

i.e... Right now he's mixing two items with the density of 48 and 70, next batch he has to mix will have different densities but the densities will be known, such as 40 and 65. So he needs a formule to put in the new densities and then have it calculate the volume of each material he needs to reach the magic number of 52.

That's how I was reading his post.

OP, let me know if I'm wrong on this.

Either way, this was the fix I had... Just plug in the density of the two materials (since I thought they were known but may change between the materials) and easter egg it.

This macro also allows the changing of the max volume and density goal.

[tbmac61]

I was reading this part as the material density may change, but he knows the density of the item he'll be mixing..

i.e... Right now he's mixing two items with the density of 48 and 70, next batch he has to mix will have different densities but the densities will be known, such as 40 and 65. So he needs a formule to put in the new densities and then have it calculate the volume of each material he needs to reach the magic number of 52.

That's how I was reading his post.

OP, let me know if I'm wrong on this.

Either way, this was the fix I had... Just plug in the density of the two materials (since I thought they were known but may change between the materials) and easter egg it.

This macro also allows the changing of the max volume and density goal.

Thank you very much! It works great!

[arlu1201]

Based on your last post in this thread, its apparent that you are satisfied with the solution(s) you've received and have solved your question, but you haven't marked your thread as "SOLVED". I will do it for you this time.

In future, to mark your thread as Solved, you can do the following -
Select Thread Tools-> Mark thread as Solved.

Incase your issue is not solved, you can undo it as follows -
Select Thread Tools-> Mark thread as Unsolved.

Also, since you are relatively new to the forum, i would like to inform you that you can thank those who have helped you by clicking the small star icon located in the lower left corner of the post which helped you. This adds to the reputation of the person who has taken the time to help you.