SOLUTION: You invested a total of $15,000 at 3% and 4.5% simple interest. During one year, the two accounts earned $600. How much did you invest in each account?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: You invested a total of $15,000 at 3% and 4.5% simple interest. During one year, the two accounts earned $600. How much did you invest in each account?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1067791: You invested a total of $15,000 at 3% and
4.5%
simple interest. During one year, the two accounts earned $600. How much did you invest in each account?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +P%5B1%5D+ = amount invested @ 3%
+P%5B2%5D+=+15000+-+P%5B1%5D+ = amount invested @ 4.5%
----------------------------------------
Use +I+=+P%2Ar%2At+
+t+=+1+ yr
+r%5B1%5D+=+.03+
+r%5B2%5D+=+.045+
(1) +I%5B1%5D+%2B+I%5B2%5D+=+600+
------------------
+I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+
+I%5B1%5D+=+P%5B1%5D%2A.03%2A1+
(2) +I%5B1%5D+=+.03P%5B1%5D+
and
(3) +I%5B2%5D+=+P%5B2%5D%2A.045%2A1+

By substitution:
+600+-+.03P%5B1%5D+=+675+-+.045%2AP%5B1%5D+
+.015P%5B1%5D+=+75+
+P%5B1%5D+=+5000+
and
+P%5B2%5D+=+15000+-+P%5B1%5D+
+P%5B2%5D+=+15000+-+5000+
+P%5B2%5D+=+10000+
----------------------------
$5,000 = amount invested @ 3%
$10,000 = amount invested @ 4.5%
-----------------------------------
check:
(2) +I%5B1%5D+=+.03P%5B1%5D+
(2) +I%5B1%5D+=+.03%2A5000+
(2) +I%5B1%5D+=+150+
and
(3) +I%5B2%5D+=+P%5B2%5D%2A.045%2A1+
(3) +I%5B2%5D+=+.045%2A10000+
(3) +I%5B2%5D+=+450+
and
(1) +I%5B1%5D+%2B+I%5B2%5D+=+600+
(1) +150+%2B+450+=+600+
(1) +600+=+600+
OK