# Kate and her Son's Age Puzzle - Solution

## The Puzzle:

## Our Solution:

First draw a table like this one below:

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")

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")