calculation of interest

Consider Bob first
Every year that his first $100 is invested he gets a flat$10 interest
Every year that the second deposit of $200 is invested he gets a flat$20 interest (plus the $10 that he is getting for he first$100
So this is how much he will have at then end of each year up to 10years
$110,$120, $130,$140, $150$350, $380,$410, $440,$470, $500 So after 10 years Bob has$500

Now think about Judy
n must be equal to 1,2,3,4, or 5 because otherwise 2n is more than 10 which is no good.

If n=1 then the first 100 dollars is invested for (10-1) years It will will accumulate to 100*1.08^9
the 200 is invested for (10-2) years. It will will accumulate to 200*1.08^8
Together these add up to $570. Bob only gets$500 so this is too much.

Try n=2 and see if it works.
When you get the correct n, the amount might not be exactly $500 bit it will be close.