SOLUTION: James invested some money at 14% interest. James also invested $54 more than 2 times that amount at 11%. How much is invested at each rate if James receives $1384.38 in interest af

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Question 1096860: James invested some money at 14% interest. James also invested $54 more than 2 times that amount at 11%. How much is invested at each rate if James receives $1384.38 in interest after one year?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+
+r%5B1%5D+=+.14+
+t+=+1+
------------------------
(1) +I%5B1%5D+=+P%5B1%5D%2A.14+
(2) +I%5B2%5D+=+P%5B2%5D%2A.11+
(3) +P%5B2%5D+=+2P%5B1%5D+%2B+54+
(4) +I%5B1%5D+%2B+I%5B2%5D+=+1384.38+
-----------------------------
Plug (3) into (2)
(2) +I%5B2%5D+=+%28+2P%5B1%5D+%2B+54+%29%2A.11+
Plug (1) and (2) into (4)
(4) +.14P%5B1%5D+%2B+.22P%5B1%5D+%2B+5.94+=+1384.38+
(4) +.36P%5B1%5D+=+1378.44+
(4) +P%5B1%5D+=+3829+
and
(3) +P%5B2%5D+=+2%2A3829+%2B+54+
(3) +P%5B2%5D+=+7658+%2B+54+
(3) +P%5B2%5D+=+7712+
---------------------------
(1) +I%5B1%5D+=+.14%2A3829+
(1) +I%5B1%5D+=+536.06+
and
(2) +I%5B2%5D+=+.11%2A7712+
(2) +I%5B2%5D+=+848.32+
----------------------------
$3,829 invested @ 14%
$7,712 invested @11%
----------------------------
check:
(4) +I%5B1%5D+%2B+I%5B2%5D+=+1384.38+
(4) +536.06+%2B+848.32+=+1384.38+
(4) +1384.38+=+1384.38+
OK