SOLUTION: The total annual income from two investments, one paying 15% annual interest and the 12%, is 1590. If the interest rates were interchanged, the total annual income would be 1650. F

Algebra ->  Test -> SOLUTION: The total annual income from two investments, one paying 15% annual interest and the 12%, is 1590. If the interest rates were interchanged, the total annual income would be 1650. F      Log On


   

Question 792867: The total annual income from two investments, one paying 15% annual interest and the 12%, is 1590. If the interest rates were interchanged, the total annual income would be 1650. Find the amount of each investments.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = amount invested @ 15%
Let +b+ = amount invested @ 12%
-----------------
In the 1st case:
(1) +.15a+%2B+.12b+=+1590+
(2) +.12a+%2B+.15b+=+1650+
------------------------
(1) +15a+%2B+12b+=+159000+
(2) +12a+%2B+15b+=+165000+
Multiply both sides of (1) by +4+
and both sides of (2) by +5+
Then subtract (1) from (2)
-----------------------
(2) +60a+%2B+75b+=+825000+
(1) +-60a+-+48b+=+-636000+
+27b+=+189000+
+b+=+7000+
-------------
Plug this result back into either (1) or (2)
(1) +15a+%2B+12b+=+159000+
(1) +15a+%2B+12%2A7000+=+159000+
(1) +15a+=+159000+-+84000+
(1) +15a+=+75000+
(1) +a+=+5000+
----------------
$5,000 was invested @ 15%
$7,000 was invested @ 12%
-----------------------
check answers:
(1) +.15a+%2B+.12b+=+1590+
(1) +.15%2A5000+%2B+.12%2A7000+=+1590+
(1) +750+%2B+840+=+1590+
(1) +1590+=+1590+
Ok
You can check other equation