Emily has 32 grams of a 25% sugar syrup, but this is just too sweet for her! how much pure water should she add to have a 10% syrup?

32 grams = water mass + sugar mass . 100% syrup=75% water+ 25%sugar 
original water content= 32*75/100=24 grams
original sugar content= 32*25/100= 8grams 

total mass at 10% syrup:
8grams/total mass=10%=0.1
total mass=8/0.1=80grams
total mass of water=80grams- 8grams of sugar content= 72 grams
total mass of water added=72grams- 24grams original water content= 48grams.

48grams

By this information, we know: (just so you know, when I will write the equation, the multiplication sign will be ^)

25%+0%=10%
32g    xg   (32+x)g
Now, we create an equation:

(0.25^32)+(0^x)=0.1^(32+x)
8+0=3.2+0.1x
8=3.2+0.1x
4.8=0.1x
48=x
48 gram.