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Kate and her Son's Age Puzzle - Solution
The Puzzle:
5 years ago Kate was 5 times as old as her Son.
In 5 years her age will be 8 less than three times her Son's age at that time.
Find their ages.
(Puzzle contributed by "Pratibha")
Our Solution:
First draw a table like this one below:
| 5 YRS AGO | PRESENT | 5 YRS LATER | |
|---|---|---|---|
| KATE | 5x | 5x + 5 | 5x + 10 |
| SON | x | x + 5 | x + 10 |
Now we know that in 5 years her age will be 8 less than three times her Son's age at that time.
So, if we add 8 to (Kate's age 5 years from now), it will be equal to 3 times (her Son's age 5 years from now) and then we can use algebra to solve it!
So:
(5x + 10) + 8 = 3(x + 10)
5x + 18 = 3x + 30
5x - 3x = 30 - 18
2x = 12
x = 12 / 2
x = 6
Now Kate's Present age is 5x + 5
=> 5(6) + 5
= 30 + 5
= 35 YEARS!!
Now her Son's Present age is x + 5
=> 6 + 5
= 11 YEARS!!
SOLVED!
(Solution contributed by "Pratibha")