
solving for proportions
Seasons greetings!
I apologize for the format of this post. The FAQ link on how to format equations seems to be broken.
I have a "compound" (C1) that is to be made from two other compounds and two pure elements (C2, C3, L, T)
Compound 2 is composed of elements in this proportion: C2 = 30X + 70L
Compound 3 is composed of elements in this proportion: C3 = 4X + Z + 95L
The final compound must have the following proportion of elements:
C1 = 8X + 2T + .2Z +89.8L
So, to find the proportions needed to make compound C1, I would need to solve the following for a, b, c, and d?
C1 = aC2 + bC3 + cL + dT
I this makes no sense, I'm sorry. My head is already hurting...(Headbang)

Hello, scunning!
We have: . . . . . . . . . . .
.
. .
. . . .
Equate coefficients: .
And solve the system of equations: .
Therefore, we will use: .

Soroban, you are a lifesaver! Thank you so much for the explanation. This forum is a wonderful resource.
Have a great Christmas!
Edit: It didn't seem like those proportions worked, but then I realized that since I expressed the compounds in terms of 100 parts, the elements needed to be expressed the same way. I change it to the following, and your logic worked perfectly! Thanks again.
C1 = aC2 + bC3 + c100L + d100T