Answer :
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
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