Question 514471

Let
Present age of father = f
Present age of  John = j
Present age of Carmen = c
Present age of Mother = m

John’s father is four times as old as John. 
f=4j
f/4=j
j=f/4........(1)
John is three years older than his sister Carmen. 
c=j-3.......(2)
John’s Mother is six times as old as Carmen. 
m=6c.........(3)
John’s father is two years older than his Mom. 
f=m+2.........(4)
Put the value of c from (2) to (3)
m=6(j-3)
Put the value of j from (1) to above equation
m=6((f/4)-3)
m=3f/2-18........(5)
Put the value of m from (5) to (4)
f=(3f/2-18)+2.........(4)
f=(3f-36)/2 + 2
f=((3f-36)+4)/2
2f=(3f-36)+4
2f=3f-36+4
2f-3f=-36+4
-f=-32
Multiply by (-1) both sides
(-1)(-f)=(-1)(-32)
f=32
Put the value of f in (1)

j=f/4........(1)
j=32/4
j=8
Put the value of j in (2)
c=j-3.......(2)
c=8-3
c=5
Put the value of c in (3)
m=6c.........(3)
m=6*5
m=30
Present age of father = f = 32 years old
Present age of Mother = m = 30 years old
Present age of  John = j = 8 years old
Present age of Carmen = c = 5 years old