SOLUTION: Juanita invests $10,000 in three different ways. With part of the money she purchases mutual funds that yield 8%. The second part, which is twice that of the second, she buys feder

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Question 1084875: Juanita invests $10,000 in three different ways. With part of the money she purchases mutual funds that yield 8%. The second part, which is twice that of the second, she buys federal bonds that yield 9%. She invests the rest in a bank at 5% interest. The first year she earns $830 in interest. How much did she invest each way?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The sentence " The second part, which is twice that of the second,
she buys federal bonds that yield 9% " I assume needs the change
" which is twice that of the first "
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Let +P%5B1%5D+=+x+ = amount invested at 8%
+P%5B2%5D+=+2x+ = amount invested at 9%
+P%5B3%5D+=+10000+-+3x+ = amount invested at 5%
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I assume each investment is simple interest
+t+=+1+ yr
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+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+
+I%5B1%5D+=+x%2A.08%2A1+
+I%5B1%5D+=+.08x+
----------------------
+I%5B2%5D+=+P%5B2%5D%2Ar%5B2%5D%2At+
+I%5B2%5D+=+2x%2A.09%2A1+
+I%5B2%5D+=+.18x+
----------------------
+I%5B3%5D+=P%5B3%5D%2Ar%5B3%5D%2At+
+I%5B3%5D+=+%28+10000+-+3x+%29%2A.05%2A1+
+I%5B3%5D+=+500+-+.15x+
------------------------------
+I%5B1%5D+%2B+I%5B2%5D+%2B+I%5B3%5D+=+830+
+.08x+%2B+.18x+%2B+500+-+.15x+=+830+
+.11x+=+330+
+x+=+3000+
and
+2x+=+6000+
and
+10000+-+3x+=+10000+-+9000+
+10000+-+3x+=+1000+
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the investments were:
$3,000 @ 8%
$6,000 @ 9%
$1,000 @ 5%
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check answers:
+I%5B1%5D+%2B+I%5B2%5D+%2B+I%5B3%5D+=+830+
+.08x+%2B+.18x+%2B+500+-+.15x+=+830+
+.08%2A3000+%2B+.18%2A3000+%2B+500+-+.15%2A3000+=+830+
+240+%2B+540+%2B+500+-+450+=+830+
+830+=+830+
OK