SOLUTION: James invested some money at 5% interest. James also invested $⁢221 more than 2 times that amount at 7%. How much is invested at each rate if James receives $850.52 in intere

Algebra ->  Finance -> SOLUTION: James invested some money at 5% interest. James also invested $⁢221 more than 2 times that amount at 7%. How much is invested at each rate if James receives $850.52 in intere      Log On


   

Question 1093436: James invested some money at 5% interest. James also invested $⁢221 more than 2 times that amount at 7%. How much is invested at each rate if James receives $850.52 in interest after one year? (Round to two decimal places if necessary.)

Found 2 solutions by josmiceli, addingup:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use +I+=+P%2Ar%2At+
Let +P%5B1%5D+ = amount invested @ 5%
+P%5B2%5D+=+2%2AP%5B1%5D+%2B+221+ = amount invested @ 7%
+t+=+1+ = 1 year
Let +I%5B1%5D+ = interest made @ 5% for 1 yr
+I%5B2%5D+=+850.52+-+I%5B1%5D+ = interest made at 7% for 1 yr
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+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+
+I%5B1%5D+=+P%5B1%5D%2A.05%2A1+
(1) +I%5B1%5D+=+.05P%5B1%5D+
-------------------------
+850+-+I%5B1%5D+=+%28+2P%5B1%5D+%2B+221+%29%2A.07%2A1+
+850.52+-+I%5B1%5D+=+.14P%5B1%5D+%2B+15.47+
(2) +I%5B1%5D+=+-.14P%5B1%5D+%2B+835.05+
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Set (1) = (2)
+.05P%5B1%5D+=+-.14P%5B1%5D+%2B+835.05+
+.19P%5B1%5D+=+835.05+
+P%5B1%5D+=+4395+
and
+P%5B2%5D+=+2P%5B1%5D+%2B+221+
+P%5B2%5D+=+2%2A4395+%2B+221+
+P%5B2%5D+=+8790+%2B+221+
+P%5B2%5D+=+9011+
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$4,395 invested @ 5%
$9,011 invested @ 7%
-------------------------
check:
+I%5B1%5D+=+4395%2A.05+
+I%5B1%5D+=+219.75+
and
+I%5B2%5D+=+9011%2A.07+
+I%5B2%5D+=+630.77+
--------------------------
+I%5B1%5D+%2B+I%5B2%5D+=+219.75+%2B+630.77+
+I%5B1%5D+%2B+I%5B2%5D+=+850.52+
OK

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Let some money be x.
1) So the amount invested at 5% will be 0.05x.
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2) He invested the rest of the money at 7%. And the problem says this amount is 221 more than 2 times x: 0.07(2x+221)
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Put these two together:
0.05x + 0.07(2x+221) = 850.52
0.05x + 0.07(2x + 221) = 850.52
0.05x + 0.14x + 15.47 = 850.52
0.19x = 835.05
x = 4395 This is the amount invested at 5%
At 7%: (2*4395)+221 = 9011
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let's check to see if I got you the right answer:
(0.05(4395)) + (0.07(9011)) = 850.52 Correct