Question

Nick has $40 and spends $1.50 each day. Bob has only $9 but he gets a daily allowance from which he saves $1.50 each day. In how many days will Bob have more money than Nick?

Answer 1

Even tho' this problem requires an inequality, let's write equations instead:

Nick's money:  $40 - ($1.50 / day)(x)              where x represents # of days
Bob's Money:   $ 9 + ($1.50 / day)(x)

Equate these two expressions:   40 - 1.50x = 9 + 1.50x

Then 31 = 3.00x, and x = 31/3 = 10 1/3 days

The two boys will have the same amount after 10 1/3 days; after that, Bob will have more (since he continues to receive an allowance and Nick continues to spend the money he already has).

Answer 2

5 days nick will have 32.50 dollars and Bob will have 16.5.
After 10 days nick will have 25 dollars and Bob will have 24 dollars
On the 11th day Nick will have 23.50 dollars and Bob will have 25.5 dollars. 
It will take bob 11 days to have more money than nick.