SOLUTION: If $50,000 is invested part at 9% and the rest at 12%, and the interest from one year is $4,800. How much was invested at 12%?

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Question 1108639: If $50,000 is invested part at 9% and the rest at 12%, and the interest from one year is $4,800. How much was invested at 12%?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +P+ = amount invested @ 9%
+50000+-+P+ = amount invested @ 12%
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Let +I+ = interest for 1 yr from 9% investment
+4800+-+I+ = interest for 1 yr from 12% investment
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Use simple interest formula
(1) +I+=+P%2A.09%2A1+
(1) +I+=+.09P+
and
(2) +4800+-+I+=+%28+50000+-+P+%29%2A.12%2A1+
(2) +4800+-+I+=+6000-+.12P+
(2) +.12P+%2B+4800+=+I+%2B+6000+
(2) +.12P+=+I+%2B+1200+
(2) +P+=+%28+25%2F3+%29%2AI+%2B+10000+
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( 1 ) +P+=+%28+100%2F9+%29%2AI+
Plug (1) into (2)
(2) +%28+100%2F9+%29%2AI+=+%28+75%2F9+%29%2AI+%2B+10000+
(2) +100I+=+75I+%2B+90000+
(2) +25I+=+90000+
(2) +I+=+3600+
and
(1) +P+=+%28+100%2F9+%29%2A3600+
(1) +P+=+40000+
and
+50000+-+P+=+50000+-+40000+
+50000+-+P+=+10000+
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$10,000 was invested @ 12%
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check:
(1) +I+=+.09P+
(1) +3600+=+.09%2A40000+
(1) +3600+=+3600+
and
(2) +.12P+=+I+%2B+1200+
(2) +.12%2A40000+=+3600+%2B+1200+
(2) +4800+=+3600+%2B+1200+
(2) +4800+=+4800+
OK