SOLUTION: A person invested $20,000, part at an interest rate of 6% annually and the remainder at 7% annually. The total interest at the end of 1 year was equivalent to an annual 6.75% rate

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Question 683584: A person invested $20,000, part at an interest rate of 6% annually and the remainder at 7% annually. The total interest at the end of 1 year was equivalent to an annual 6.75% rate on the entire $20,000. How much was invested at each rate?

Answer by mananth(16949) (Show Source):
You can put this solution on YOUR website!
6.75% on 20,000 = 1350 total interest earned.

Part I 6.00% per annum ------------- Amount invested =x
Part II 7.00% per annum ------------ Amount invested = y
20000
Interest----- 1350

Part I 6.00% per annum ---x
Part II 7.00% per annum ---y
Total investment
x + 1 y= 20000 -------------1
Interest on both investments
6.00% x + 7.00% y= 1350
Multiply by 100
6 x + 7 y= 135000.00 --------2
Multiply (1) by -6
we get
-6 x -6 y= -120000.00
Add this to (2)
0 x 1 y= 15000
divide by 1
y = 15000
Part I 6.00% $ 5000
Part II 7.00% $ 15000

CHECK
5000 --------- 6.00% ------- 300.00
15000 ------------- 7.00% ------- 1050.00
Total -------------------- 1350.00

m.ananth@hotmail.ca