# Kate and her Son's Age Puzzle - Solution

### 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")

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")

### Our Solution:

First draw a table like this one below:

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")

5 YRS AGO | PRESENT | 5 YRS LATER | |
---|---|---|---|

KATE | 5x | 5x + 5 | 5x + 10 |

SON | x | x + 5 | x + 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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