Elizabeth, Ellen, and David are siblings. Elizabeth is two years older than Ellen and David is 1-year less than half the age of Ellen. If the sum of their ages is 31, how old is Elizabeth?

Answer 1

Let x = Elizabeth's age, y = Ellen's age and z = Davids age. It is asking for Elizabeth's age, x.

From the description:

x + y + z = 31

x = y + 2

z = y/2 -1

Substituting the second and third equation into the first equation:

(y+2) +y + y/2 -1 = 31 --> 5y/2 = 30 --> y = (2/5)30 = 12

x = y +2 = 12 + 2 = 14

So Elizabeth is 14

Note: David = z = y/2-1 = 12/2-1 = 5

14 + 12 + 5 = 31

Answer 2

x+(x+2)+(x/2-1)=31

2.5x+1=31

2.5x=30

x=12

14

5