Increase amount of ingredients to keep concentration after dilution

[coo1guy]

I make a drink using 13.5g/L of some South American tea (yerba) and 65g/L of sugar.

I now want this drink to be slightly carbonated, so I'll fill the first 1/3 of the glass with sparkling water and the rest with my drink.

I'm looking for the new amounts of the two ingredients per liter, so that, after the 1/3 2/3 dilution, the drink will keep its 13.5g/L yerba and 65g/L sugar concentrations.

If you can describe me the equation, that would be cool, because I'm not sure yet 1/3 will be the exact dilution.

Thanks

 

[Deleted member 4993]

I make a drink using 13.5g/L of some South American tea (yerba) and 65g/L of sugar.

I now want this drink to be slightly carbonated, so I'll fill the first 1/3 of the glass with sparkling water and the rest with my drink.

I'm looking for the new amounts of the two ingredients per liter, so that, after the 1/3 2/3 dilution, the drink will keep its 13.5g/L yerba and 65g/L sugar concentrations.

If you can describe me the equation, that would be cool, because I'm not sure yet 1/3 will be the exact dilution.

Thanks

Suppose you made a Litre of drink using the old recipe.

Now you pour out 1/3 L and 2/3 L is left.

Amount of tea poured out = 1/3 * 13.5 = 4.5 gms

Amount of sugar poured out = 1/3 * 65 = 21.67 gms

When you pour in 1/3 L of carbonated water you would have to add back in the amounts of tea and sugar (calculated above).

 

[coo1guy]

Suppose you made a Litre of drink using the old recipe.

Now you pour out 1/3 L and 2/3 L is left.

Amount of tea poured out = 1/3 * 13.5 = 4.5 gms

Amount of sugar poured out = 1/3 * 65 = 21.67 gms

When you pour in 1/3 L of carbonated water you would have to add back in the amounts of tea and sugar (calculated above).

Genius!
Thank you