Question 1193747
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Part A


s = son's present age
3s = Jonathan's present age (3 times as old)


Rewind the clock twelve years
s-12 = son's age twelve years ago
3s-12 = Jonathan's age twelve years ago


Now we use the fact that "Twelve years ago, he was six times as old as his son was" to get...


Father's age 12 years ago = 6*(son's age 12 years ago)
3s-12 = 6*(s-12)
3s-12 = 6s-72
-12+72 = 6s-3s
60 = 3s
s = 60/3
s = 20
The son is currently 20 years old
3s = 3*20 = 60
The father (Jonathan) is currently 60 years old.


Twelve years ago the father and son were 60-12 = 48 and 20-12 = 8 years old respectively.
Notice how the jump from 8 to 48 is "times 6" which helps us confirm the answers.


Answers:
Jonathan's current age = 60
Son's current age = 20


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Part B


d = Dave's age nine years ago
5d = Jareth's age nine years ago (5 times as much)


Fast forward to the present, i.e. add on nine years
d+9 = Dave's current age
5d+9 = Jareth's current age


"now, he (Jareth) is only 3 times as old as Dave"
So,
Jareth's current age = 3*(Dave's current age)
5d+9 = 3*(d+9)
5d+9 = 3d+27
5d-3d = 27-9
2d = 18
d = 18/2
d = 9
Dave was 9 years old 9 years ago
Therefore, he is currently 9+9 = 18 years old now.
I.e. d+9 = 9+9 = 18 is his current age


Jareth is currently 5d+9 = 5*9+9 = 54 years old.
Nine years ago, he was 54-9 = 45 


The jump from 9 to 45 is "times 5".
The jump from 18 to 54 is "times 3".



Answers:
Jareth's current age = 54
Dave's current age = 18


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Part C


x = Malou's current age
y = Mildred's current age


x+8 = Malou's age eight years from now
y+8 = Mildred's age eight years from now


"Eight years from now, Malou will be as old as Mildred is now"
This means,
Malou's future age = Mildred's current age
x+8 = y
y = x+8


"Eight years from now,...Mildred will be three times as old as Malou is now."
Meaning,
Mildred's future age = 3*(Malou's current age)
y+8 = 3*(x)
y+8 = 3x


Plug in y = x+8 and solve for x
y+8 = 3x
x+8+8 = 3x
x+16 = 3x
16 = 3x-x
16 = 2x
2x = 16
x = 16/2
x = 8
Malou is currently 8 years old


So,
y = x+8
y = 8+8
y = 16
making Mildred to be 16 years old currently


Eight years from now, Malou is 8+8 = 16 which matches with Mildred's current age. That confirms the first part.


Also, eight years from now, Mildred will be 16+8 = 24 years old which is exactly 3 times that of Malou's current age (8). Therefore, the answers have been fully verified.



Answers:
Malou's current age = 8
Mildred's current age = 16
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