Brain blocked on recalling this formula

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SUMMARY

The discussion focuses on calculating the mass of two fluids, m1 and m2, in a mixing fluid calculator when the total volume (mt) and temperatures (T1, T2, Tf) are known. The user seeks to derive the formula for m2 while also solving for m1 simultaneously. The proposed formula for m2 is m2 = m1 (T1 - Tf) / (Tf - T2). This formula allows for the calculation of both m1 and m2 based on the known parameters of the mixture.

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TL;DR
Need to manipulate T(final) = (m1_T1 + m2_T2) / (m1 + m2) to solve for m2
Trying to build a mixing fluid calculator and cannot for the life of me figure out how to solve for m2 rather then Tf

Got an answer to question 1, but bonus question: is there anyway to solve for m2 and m1 if mt is known?

IE given a total volume of mixture IE 99ml, at 20 deg. I know T1 is 25 deg, and T2 is 10.. Using the math it tells me I need 33ml of T2 and 66ml of T1. This will be built into a spreadsheet, is there anyway to calculate both t1 and t2 at the same time?
 
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I suggest it is,
m2 = m1 (T1 - Tf) / (Tf - T2)
 
tech99 said:
I suggest it is,
m2 = m1 (T1 - Tf) / (Tf - T2)
Thank you so much!
 
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