SOLUTION: Phyllis invested $13,500, a portion earning a simple interest rate of 4 1/2% per year and the rest earning a rate of 4% per year. After 1 year the total interest earned on these

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Question 1141073: Phyllis invested $13,500, a portion earning a simple interest rate of
4 1/2% per year and the rest earning a rate of 4% per year. After 1 year the total interest earned on these investments was $585. How much money did she invest at each rate?
$______at 4 1/2%
$______at 4%

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +P+ = Amt invested @ +4.5+%
+13500+-+P+ = Amt invested @ +4+%
Let +I+ = interest earned @ +4.5+%
+585+-+I+ = interest earned @ +4+%
--------------------------------------------------
+I+=+P%2Ar%2At+
(1) +I+=+P%2A.045%2A1+
(2) +585+-+I+=+%28+13500+-+P+%29%2A.04%2A1+
-----------------------------------------------
(2) +585+-+.045P+=+540+-+.04P+
(2) +.005P+=+45+
(2) +P+=+9000+
and
+13500+-+P+=+13500+-+9000+
+13500+-+P+=+4500+
------------------------------------
$9,000 @ 4.5%
$4,500 @ 4%
----------------------
check:
+I+=+.045%2A9000+
+I+=+405+
and
+585+-+I+=+585+-+405+
+585+-+I+=+180+
+180+-+4500%2A.04+
+180+=+180+
OK