Ann invested $12,000 in two bank accounts. One of the accounts pays 6% annual interest, and the other account pays 5% annual interest. If the combined interest earned in both accounts after a year was $700, how much money was invested in each account?

*What are we trying to find in this problem?*

We want to know the amount of money invested in each account-- in other words, we want to know the amount invested in the 6% account and the amount invested in the 5% account. Each of the things we are trying to find will be represented by a variable:

x = amount invested at 6%

y = amount invested at 5%

Since we have two variables to solve for, we will need to find a system of two equations to solve.

*How do we find the two equations we need?*

We are given two numbers in the problem:

$12,000 = total money invested in both accounts

$700 = total interest earned in both accounts

Let's start with the $12,000. Ann wants to split this money into two parts. We have chosen to call the two parts x and y. Since these two parts must total to $12,000, this gives us our first equation:

**x + y = 12,000**

Now let's look at the $700, the interest earned on the two accounts together. Let's think about the formula for calculating simple interest :

Interest = (Principle)(Rate)(Time)

Since the time period in this problem is one year, our simple interest equation becomes:

Interest = (Principle)(Rate)(1)

or

Interest = (Principle)(Rate)

Each account has a different amount of money invested in it (either x dollars or y dollars), and each account has a different interest rate (either 6% or 5%). This gives us the following:

Interest earned on x dollars = (x)(6%) = .06x

and

Interest earned on y dollars = (y)(5%) = .05y

The total interest earned in both accounts is $700, so our second equation is:

Interest earned on x dollars + interest earned on y dollars
= total interest

.06x + .05y = 700

If we multiply both sides of this equation by 100 to clear
the decimals, it becomes:
**6x + 5y = 70,000**

Now we'll solve the system of equations:

x + y = 12,000

6x + 5y = 70,000

Multiply the first equation by -5, then add the equations:

-5x - 5y = -60,000
__6x + 5y = 70,000__

x = 10,000

Ann invested $10,000 in the account that pays 6% interest.

To find the amount invested in the other account, substitute 10,000 for x in either of our equations. We'll choose the easier equation:

x + y = 12,000

10,000 + y = 12,000

y = 2,000

Ann invested $2,000 in the account that pays 5% interest.