Sam has 100$ in the bank and deposits $18 per month. Gil has $145 in the bank and deposits $15 per month. In how many months will Gil have a larger bank balance than sam?

The accounts will be equal in 15 months.

Explanation:

So, Gil will have a larger balance than Phillip for 14 months.

Here's how I got there:

I'm letting "x" be the variable that represents the number of months, and I'm setting up two expressions, one for Phillip:

100+18x,

and one for Gil:

145+15x .

100 and 145 are the starting balances, 18 and 15 are the amounts each is depositing into his account each month, for "x" number of months.

I'm going to set these expressions equal to each other:

100+18x=145+15x.

(1) Subtract  

15x

from both sides:

100+3x=145.

Subtract  

100

from both sides:

3x=45.

(3) Divide both sides by  

3x=15

This is the number of months at which the account balances will be equal.