SOLUTION: An actor invests some money at 8%, and $41000 more than four times the amount at 9%. The total annual interest earned from the investment is $60010. How much did he invest at each

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Question 1109456: An actor invests some money at 8%, and $41000 more than four times the amount at 9%. The total annual interest earned from the investment is $60010. How much did he invest at each amount? Use the Six Step Method.
He invested $_ at 8% and $_ at 9%.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use simple interest formula
+I+=+P%2Ar%2At+
------------------
Investment @ 8%
(1) +i+=+P%2A.08%2A1+
Tnvestment @ 9%
(2) +6001+-+I+=+%28+4P+%2B+41000+%29%2A.09%2A1+
-----------------------------------------
Plug (1) into (2)
(2) +6001+-+.08P+=+.36P+%2B+3690+
(2) +.44P+=+2311+
(2) +P+=+5252.27+
and
(1) +I+=+.08%2A5252.27+
(1) +I+=+420.18+
and
+4P+%2B+41000+=+4%2A5252.27+%2B+41000+
+4P+%2B+41000+=+21009.08+%2B+41000+
+4P+%2B+41000+=+62009.08+
---------------------------------------
He invested $5,252.27 @ 8% and
$62,009.08 @ 9%
---------------------------------------
check answer:
(2) +6001+-+I+=+%28+4P+%2B+41000+%29%2A.09%2A1+
(2) +6001+-+420.18+=+%28+4%2A5252.27+%2B+41000+%29%2A.09%2A1+
(2) +5580.82+=+%28+21009.08+%2B+41000+%29%2A.09+
(2) +5580.82+=+62009.08%2A.09+
(2) +5580.82+=+5580.82+
and
(1) +I+=+.08P+
(1) +420.18+=+.08%2A5252.27+
(1) +420.18+=+420.18+
OK