The sample problem here is....You have a total of $8000 invested in two simple interest accounts. On one account; a money market fund, and annual simple interest rate is 11.5%. On the second account; a bond fund, the annual simple interest rate is 9.75%. The total annual interest earned by the two accounts is $823.75. How much have you invested in each account?

In the book they have a little chart I will try to draw:

Principal Interest Interest earned

Amount @ 11.5% | x | 0.115 | .115x

Amount @ 9.75% |8000 - x | 0.0975 | .0975(8000-x)

Then the equation below it is:

.115x+.0975(8000-x) = 823.75

.115x + 780 -.0975 = 823.75 (This I understand, multiply to get rid of the parenthesis)

.0175x + 780 = 823.75 (Subtract from each side; .110 - .0975 = .0175)

0.175x = 43.75 (subtract the whole numbers; 823.75 - 780 = 43.75)

x = 2500

The amount invested at 9.75% is 8000 - x

Replace x with 2500 and evaluate.

8000 - x = 8000 - 2500 =5500

The amount invested at 11.5% = $2500

The amount invested at 9.75% = $5500

That lest step in the equation is where I get lost....where the fuck did that 2500 come from? Did they just guess? I just don't get it.