SOLUTION: John’s father is four times as old as John. John is three years older than his sister Carmen. John’s Mother is six times as old as Carmen. John’s father is two years older than his

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Question 514471: John’s father is four times as old as John. John is three years older than his sister Carmen. John’s Mother is six times as old as Carmen. John’s father is two years older than his Mom. How old are John, Carmen, and John’s parents.
Answer by Maths68(1474) About Me  (Show Source):
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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