Answer:
He invested $20000 for 3% rate and $15000 for 2% rate.
Step-by-step explanation:.
Let the 3% rate be for Account A and the 2% rate for Account B.
From the question, we know that the Principal from both accounts must add up to $35000
35000 ________________________ (1)
We also know that the interest from both accounts add up to $900
________________________(2)
The Interest from Account A (R = 3%, T = 1) is:
![I_A = \frac{P_A *R*T}{100}](https://tex.z-dn.net/?f=I_A%20%3D%20%5Cfrac%7BP_A%20%2AR%2AT%7D%7B100%7D)
This implies that:
________________________(3)
The Interest from Account B (R = 2%, T = 1) is:
![I_B = \frac{P_B *R*T}{100}](https://tex.z-dn.net/?f=I_B%20%3D%20%5Cfrac%7BP_B%20%2AR%2AT%7D%7B100%7D)
This implies that:
_____________________________(4)
From (1),
Putting this in (4)
________________(5)
From (2):
![I_A = 900 - I_B](https://tex.z-dn.net/?f=I_A%20%3D%20900%20-%20I_B)
Putting this in (3):
_______________________(6)
(5) and (6) are simultaneous equations, hence, we can solve them:
![100I_B +3P_A = 90000\\\\100I_B + 2P_A = 70000](https://tex.z-dn.net/?f=100I_B%20%2B3P_A%20%3D%2090000%5C%5C%5C%5C100I_B%20%2B%202P_A%20%3D%2070000)
Subtracting (5) from (6):
![3P_A - 2P_A = 90000 - 70000](https://tex.z-dn.net/?f=3P_A%20-%202P_A%20%3D%2090000%20-%2070000)
$20000
Hence:
![P_B = 35000 - 20000\\\\](https://tex.z-dn.net/?f=P_B%20%3D%2035000%20-%2020000%5C%5C%5C%5C)
$15000
Also:
![100I_B + 3P_A = 90000\\\\100I_B + (3 * 20000) = 90000\\\\100I_B + 60000 = 90000\\\\\\100I_B = 90000 - 60000\\\\100I_B = 30000](https://tex.z-dn.net/?f=100I_B%20%2B%203P_A%20%3D%2090000%5C%5C%5C%5C100I_B%20%2B%20%283%20%2A%2020000%29%20%3D%2090000%5C%5C%5C%5C100I_B%20%2B%2060000%20%3D%2090000%5C%5C%5C%5C%5C%5C100I_B%20%3D%2090000%20-%2060000%5C%5C%5C%5C100I_B%20%3D%2030000)
= $300
Hence:
![I_A = 900 - 300\\\\](https://tex.z-dn.net/?f=I_A%20%3D%20900%20-%20300%5C%5C%5C%5C)
$600
Hence, Larry invested $20000 at 3% annual interest and got $600 interest. He also invested $15000 at 2% annual interest and got $300.