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# Kate and her Son's Age - Solution

Puzzles -> Algebra Puzzles

 The Puzzle: 5 years ago Kate was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find their ages.(Puzzle contributed by "Pratibha")

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## The Solution . . .

First draw a table like this one below:

5 YRS AGOPRESENT5 YRS LATER
KATE5x5x + 55x + 10
SONxx + 5x + 10

Now we know that 5 years from now Kate's age will be 8 less than three times the corresponding age of her Son! So, if we add 8 to Kate's age , 5 years from now, and make her Son's age 3 times more we will find out 'x' and PROBLEM SOLVED!

Therefore:

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")

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