LOLLol, 7 years later, I don't think anyone else is listening. But I guess we can still learn here.
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You will only cut you nitrates in half in a 50% WC if the water you add has 0 nitrates, which is unlikely, nitrates are not like sugar, as per your example refering to saturated solutions, your nitrates will continue to climb as they are formed from organic waste coverting to nitrates, be it in your tank or as a result of poor filter maintainance, quite right feeding less may help, but algea may still grow because of low light, CO2 fluctuations, silicates leaching into the water, no plants to absorb the nitrates available etc
Your specific problem seems to be organic material somewhere in the tank diluting the clean water. In theory if you do a 50% water change it will cut the nitrates in half but you have to account for organic material inside of your tank/filter media continuously breaking down and polluting the newly added water rising the nitrate levels. If your water has lets say 20ppm then organic materials will break down faster and pollute the water faster than water that has a nitrate level of 80ppm.