Larry has an annual return of $213 from $3000 invested at simple interest, some at 5% and the rest at 8%. how much is invested at each rate?

There are two equations to express this problem. 1) expresses the total amount invested and 2) expresses the proportions of the amounts invested and how they relate to the interest earned . . .

1) x + y = 3000
2) 0.08x + 0.05y = 213

* from the first equation:

x + y = 3000

y = 3000 - x

*substitute this into the second equation

0.08x + 0.05(3000 - x) = 213

* solve for x

0.08x + 150 - 0.05x = 213

(0.08 - 0.05)x + 150 = 213

(0.03)x = 213 - 150

0.03x = 63

x = 63/0.03 = 2100

* now just substituting in for x the known value

y = 3000 - x = 3000 - 2100 = 900

This means:

$2100 was invested at 8% simple interest
$900 was invested at 5% simple interest