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a. Jonathan is now three times as old as his son is. Twelve years ago, he was six times as old as his son was. Find the present age of each.
b. Nine years ago, Jareth was five times as old as Dave. Now, he is only three times as old as Dave. Find their present ages.
c. Eight years from now, Malou will be as old as Mildred is now, while Mildred will be three times as old as Malou is now. How old are they now?
Answer by math_tutor2020(3816)   (Show Source):
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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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