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 of increase, Sarah will drink an additional 5% of 224 ounces, which is 0.05 * 224 = <<0.05*224=11.2>>11.2 ounces.
So after the first week of increase, she will drink 224 + 11.2 = <<224+11.2=235.2>>235.2 ounces of water.
Similarly, after the second week of increase, she will drink an additional 5% of 235.2 ounces, which is 0.05 * 235.2 = <<0.05*235.2=11.76>>11.76 ounces.
So after the second week of increase, she will drink 235.2 + 11.76 = <<235.2+11.76=246.96>>246.96 ounces of water.
Similarly, after the third week of increase, she will drink an additional 5% of 246.96 ounces, which is 0.05 * 246.96 = <<0.05*246.96=12.348>>12.348 ounces.
So after the third week of increase, she will drink 246.96 + 12.348 = <<246.96+12.348=259.308>>259.308 ounces of water, which rounds to the nearest ounce as 259 ounces. Answer: \boxed{259}.