Question

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

Answer 1

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 `3`:

`x = 15`

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

Now you can answer any one of three different questions:

(1) When will their bank balances be equal?
At `15` months.

(2) For how many months will Gil have a larger bank balance than Phillip?
For `14` months, because at `15` months, they will be equal.

(3) When will Phillip have more money in the bank than Gil?
At `16` months.

Connie