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total alkalinity and total hardness

I think I understand that KH measures carbonate ion concentration and GH
measures total dissolved solids. Knowing the total alkalinity and total
hardness, and the concentrations of Cl-, NO3-, SO4--, Ca++ and Mg++ can
we deduce CO3--, Na+ and K+ concentrations? (assuming typical ground
water from a well)

Here are the parameters (ppm):

Chloride       45.
Nitrate        22.2
Sulfate        24.
Barium       <  0.02
Calcium        92.
Magnesium      12.20
Ferrous Iron <  0.02
Manganese    <  0.02
Copper       <  0.02
Zinc            0.36
Chromium     <  0.02
Phosphate       0.041

Ph              7.1
Total Hardness    280
Total Alkalinity  330                           

Steve in Vancouver BC