Let:
Joe = x
Lauren = y
Emma = a
y= x/2
Therefore, 2y = x......1
a = x+4
But, since x = 2y,
Then, a = 2y+4........2
y + x + a = 54
y + 2y + 2y+4 = 54
5y + 4 = 54
5y = 54 - 4
5y = 50
y = 10
Subs y=10 into x=2y
x=2(10)
x=20
Therefore, Joe is 20 years old.