Sophie has 25 ounces of a 20% sugar syrup that she wants to dilute to a 10% sugar syrup. How much water does she need to add to obtain the 10% syrup?

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