Question 889113
Let Emma's age be "a"
    Olivia's age be "b"

a = 10 + (1/2)(b)
a = 10 + b/2

a + b = 31
10 + b/2 + b = 31
3b/2 = 21
3b = 42
b = 14

a = 10 + (1/2)(14)
a = 17

Therefore, Emma's age is 17 years old.