Sarah drinks about 224 ounces of water each week. She would like to increase this amount by 5% each week. How much water will she drink after the third week of increase?

Round your answer to the nearest ounce.

After the first week, Sarah will drink 224 + (224 * 0.05) = <<224+(224*0.05)=235.2>>235.2 ounces of water.

After the second week, Sarah will drink 235.2 + (235.2 * 0.05) = <<235.2+(235.2*0.05)=246.96>>246.96 ounces of water.
After the third week, Sarah will drink 246.96 + (246.96 * 0.05) = <<246.96+(246.96*0.05)=259.30>>259.30 ounces of water.
Therefore, Sarah will drink 259.30 ounces of water after the third week. Answer: \boxed{259}.