Solving system of equations works on V7 but not V12?

Questions
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1

Hi guys,
This question is related to solving a system of linear equations (the Specific Gravity of a mixture)
In my old version of Mathematica7 when I run the following:

Solve[{m1 + m2 == m3, v1 + v2 == v3, m1/v1 == SG1, m2/v2 == SG2, 
  m3/v3 == SG3, m1/((m1 + m2)) == Cw, SG1 == 1.35, SG2 == 1, 
  Cw == 0.52}, SG3]
output[1]: {{SG3 -> 1.15582}}

However if I run the same code in Mathematica12
I get:

a blank output, aka no answer.

What should I be doing instead to get an output in Mathematica 12? Has “Solve” changed? what should I do differently? (SG1 = solids, SG2 = Liquid(Water), SG3 = mixture, Cw = percent of solids)

Thanks,
James

SG of mixture _OP_Water+Solids_CP_.nb (4.94 KB)

2

Try:

 $Version
  (* "12.3.0 for Microsoft Windows (64-bit) (May 10, 2021)"*)

Solve is symbolic solver need exact values:

 Solve[{m1 + m2 == m3, v1 + v2 == v3, m1/v1 == SG1, m2/v2 == SG2, 
   m3/v3 == SG3, m1/((m1 + m2)) == Cw, SG1 == 135/100, SG2 == 1, 
   Cw == 52/100}, SG3, MaxExtraConditions -> All]

 (*{{SG3 -> ConditionalExpression[675/584, 
     And[-13 + 25 Cw == 0, (-12) m1 + 13 m2 == 0, (-25)
          m1 + 13 m3 == 0, -27 + 20 SG1 == 0, -1 + SG2 == 0, (-20)
          m1 + 27 v1 == 0, (-12) m1 + 13 v2 == 0, (-584)
          m1 + 351 v3 == 0]]}}*)

With numeric values gives errors,but can solve:

   Solve[{m1 + m2 == m3, v1 + v2 == v3, m1/v1 == SG1, m2/v2 == SG2, 
     m3/v3 == SG3, m1/((m1 + m2)) == Cw, SG1 == 1.35, SG2 == 1, 
     Cw == 0.52}, SG3, MaxExtraConditions -> 8]
3

Hi Mariusz,

What you suggested seems to work.
Do you have any comments on why the code I wrote wasn’t working?

4

I suppose it is the same reason why this gives an empty answer:

Solve[{a + c == 0, a - b == 0}, a]

When you solve for a, you ask for a solution of the form {{a->something}}, but it can’t. The following variant works, though, because it allows for a solution of the form {{a->something,c->something}}:

Solve[{a + c == 0, a - c == 0}]