If Sophie adds x oz of water, the volume of the new syrup will be (25 + x) oz. The syrup she starts with already contains 0.20 • (25 oz) = 5 oz of sugar, and if she adds water to it, that amount doesn't change.
She wants to end up with a syrup containing 10% sugar, so that the starting 5 oz makes of 10% of the total (25 + x) oz of syrup. So
5 / (25 + x) = 0.10
5 = 0.10 (25 + x)
5 = 2.5 + 0.10x
2.5 = 0.10x
x = 2.5 / 0.10
x = 25 oz
