SOLUTION: Katie invested a total of $4000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $136 interest. How much was invested at

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Katie invested a total of $4000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $136 interest. How much was invested at      Log On

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Question 1092177: Katie invested a total of $4000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $136 interest. How much was invested at each rate?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use +I+=+P%2Ar%2At+
+I%5B1%5D+=+P%5B1%5D%2A.03%2A1+
(1) +I%5B1%5D+=+.03P%5B1%5D+
--------------------------
and
+I%5B2%5D+=+.04P%5B2%5D+
+P%5B2%5D+=+4000+-+P%5B1%5D+
+I%5B2%5D+=+.04%2A%28+4000+-+P%5B1%5D+%29+
----------------------------
+I%5B2%5D+=+136+-+I%5B1%5D+
+136+-+I%5B1%5D+=+.04%2A%28+4000+-+P%5B1%5D+%29+
----------------------------------
+136+-+I%5B1%5D+=+160+-+.04P%5B1%5D+
(2) +I%5B1%5D+=+.04P%5B1%5D+-+24+
Plug (1) into (2)
(2) +.03P%5B1%5D+=+.04P%5B1%5D+-+24+
(2) +.01P%5B1%5D+=+24+
(2) +P%5B1%5D+=+2400+
and
+P%5B2%5D+=+4000+-+P%5B1%5D+
+P%5B2%5D+=+4000+-+2400+
+P%5B2%5D+=+1600+
---------------------
$2,400 is invested @ 3%
$1,600 is invested @ 4%
---------------------
check:
(1) +I%5B1%5D+=+.03P%5B1%5D+
(1) +I%5B1%5D+=+.03%2A2400+
(1) +I%5B1%5D+=+72+
and
(2) +I%5B2%5D+=+.04%2AP%5B2%5D+
(2) +I%5B2%5D+=+.04%2A1600+
(2) +I%5B2%5D+=+64+
-------------------------
+I%5B1%5D+%2B+I%5B2%5D+=+72+%2B+64+
+I%5B1%5D+%2B+I%5B2%5D+=+136+
OK