Soda Spar

.6Na20
.3 K2O
.1 CaO

Potash Spar
.6K20
.4 Na2O

Recipe requires .5 Na2O +.5 K2O
How much Soda and How much Potash spars do you need

s= amount of Soda Spar in Mols
p= amount of Potas Spar in Mols

a:Total Potash From Recipe=
s* 0.3+ p* 0.6 = 0.5
b:Total Soda From Recipe =
s* 0.6+ p*0.4= .5
Equation a transformed
s=.5-.6p =1.667-2p
     .3

Equation b Transformed
p=.5- .6s =1.25-1.5s
     .4
Substituting 1.667-2p for s

p=1.25- 1.5(1.667-2p)= 3p-1.25

transformed
2p=1.25
p=.625
Since s=1.667-2p, s=1.667-2* 0.625, s=.417

Checking, p=.625, s=.417

.6Na20
.3 K2O
.1 CaO

Potash Spar
.6K20
.4 Na2O

Total Potash From Recipe= s* 0.3+ p* 0.6 = 0.5
.417*.3+.625*.6=.500
Total Soda From Recipe = s* 0.6+ p*0.4= .5
.417*.6 +.625*.04=.500