10 is [tex] \frac{5}{3} [/tex] of 6.
So, we need to find 5/3 of the water she needs for 6 glasses to make 10 glasses.
5 1/2 = 11/2
[tex] \frac{11}{2} [/tex] · [tex] \frac{5}{3} [/tex] = [tex] \frac{55}{6} [/tex] = 9 [tex] \frac{1}{6} [/tex]
Therefore, she needs 9 [tex] \frac{1}{6} [/tex] cups of water to make 10 glasses of lemonade.