# Thread: simultaneous equation problem solving

1. ## simultaneous equation problem solving

John's mother is 5 times as old as John is. Three years ago, she was 9 times his age. What are their present ages?

2. Have a think.

Let John's age be $x$

His mother's age will then be $5x$

So three years ago she was nine times his age...

$5x-3 = 9(x-3)$

The $-3$ on the left side represents 3 years ago, you also have to do it on his mother's age. Since she is nine times the age just multiply the whole side by 9.

3. Thanks jgv115,

So is it:

5x-3=9(x-3)
5x-3=9x-27
27-3=9x-5x
24=4x
6=x
So John would be 6 years old and his mum would be 6x5=30

4. Indeed.

5. Thank you very, very much "jgv115".

I will no doubt have many more simple questions over the next 10months.