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Question 930254: How do i set these equations up?
An investment of $6000 is made into a 14% annual simple interest account. How much money is deposited into a 10% annual simple interest account if the total annual interest earned on both accounts is 12% of the total investment?
Also
A stockbroker has 12,000 to invest. The broker recommends part of the 12,000 be placed in 12% tax free bonds, and the rest in 18% commercial bonds. How much should be invested in the commercial bonds so that the total annual interest is $1920?
So far for the last one I got 12,000-x(.12)+.18x=$1920, but am coming up with something other than what is on the answer key.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! amount invested at 14.00% 6000
Another part invested at x% 10.00% x
14.00% * 6000 + 10.00% x= 12.00% (x+ 6000 )
840 + 10.00% x= 12.00% x+ 12.00% * 6000
840 + 10.00% x= 12.00% x+ 720
12.00% x - 10.00% x= 840 - 720
2.00% x= 120
x= 120 / 2.00%
x= 6000
The amount invested at 10.00% = $ 6000
CHECK
14.00% * 6000 + 6000 * 10.00%
840 + 600 = 1440
12000 * 12.00% = 1440
(6000+6000)
Part I 12.00% per annum ------------- Amount invested =x
Part II 18.00% per annum ------------ Amount invested = y
12000
Interest----- 1920.00
Part I 12.00% per annum ---x
Part II 18.00% per annum ---y
Total investment
x + 1 y= 12000 -------------1
Interest on both investments
12.00% x + 18.00% y= 1920
Multiply by 100
12 x + 18 y= 192000.00 --------2
Multiply (1) by -12
we get
-12 x -12 y= -144000.00
Add this to (2)
0 x 6 y= 48000
divide by 6
y = 8000
Part I 12.00% $ 4000
Part II 18.00% $ 8000
CHECK
4000 --------- 12.00% ------- 480.00
8000 ------------- 18.00% ------- 1440.00
Total -------------------- 1920.00
m.ananth@hotmail.ca
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