$3000 at 10%
$2400 at 8%
A substitution will work here
Total Principal = 5400
Let x = amount invested at 10%
Let y = amount invested at 8%
So
x + y = 5400
y = 5400 -x
Total yield after one year is $492.00
So we have
0.10x + 0.08y = 492
Substitute 5400 -x for y to get everything in terms of x
0.10x + .08(5400 - x) = 492
0.10x + 432 - 0.08x = 492
Combine like terms
0.02x + 432 = 492
Subtract 432 from both sides of the equation
0.02x = 492 - 432
0.02x = 60
Divide both sides by 0.02
x = 60/.02
x = 3000
y = 5400 -x = 5400 - 3000= 2400
y = 2400
Checking
0.10(3000) n+ 0.08(2400) = 492
300 + 192 = 492
492 = 492
You can also use elimination to solve this problem
I hope you find this useful if you have any questions send me a message.