Since no sugar will be added or removed, the number or moles of it in the glas won't change.
Let's call this quantity:
The molar concetrnation can be written as the followin equation:
Where C is the concentration given the number of moles of sugar and the volume V.
We can rewrite this as:
Now, before the ice melts, the volume of the lemonate is 150 mL and the sugar concentration is 2.27 mol/L. Let's call this situation 1:
After the ice melt the one third it will, we will have a certain volume and the concentration we want 1.88 mol/L. Let's call this situation 2:
Now, we can put thouse tofether:
And we can solve for the unknown volume of situation 2:
Since the final volume is approximately 181 mL, the difference between it and the initial volume is the volume of water that came from the melted part of the ice:
Since we assume that the density of the water is 1.00 g/mL, we can calculate the mass it represents:
And since this is only 1 third of the ice (the rest won;t melt), we know that the whole ice will have three times this mass:
So, it should be added approximatelt 93 grams of ice.