SOLUTION: A real estate firm invests $100,000 in two ways. The first portion is invested with an annual return of 8%. The rest is invested for an annual return of 5%. The firm wants an annua

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Question 803721: A real estate firm invests $100,000 in two ways. The first portion is invested with an annual return of 8%. The rest is invested for an annual return of 5%. The firm wants an annual income of $6800 from the investments. How much should be put into each investment.
Answer by mananth(16946) About Me  (Show Source):
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Part I 8.00% per annum ------------- Amount invested =x
Part II 5.00% per annum ------------ Amount invested = y
100000
Interest----- 6800.00

Part I 8.00% per annum ---x
Part II 5.00% per annum ---y
Total investment
x + 1 y= 100000 -------------1
Interest on both investments
8.00% x + 5.00% y= 6800
Multiply by 100
8 x + 5 y= 680000.00 --------2
Multiply (1) by -8
we get
-8 x -8 y= -800000.00
Add this to (2)
0 x -3 y= -120000
divide by -3
y = 40000 - x)
Part I 8.00% $ 60000
Part II 5.00% $ 40000

CHECK
60000 --------- 8.00% ------- 4800.00
40000 ------------- 5.00% ------- 2000.00
Total -------------------- 6800.00