SOLUTION: A businessman has invested $100,000 at 8% and $150,000 at 12% simple interest. At what rate must he invest $200,000 for him to earn 10% overall?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: A businessman has invested $100,000 at 8% and $150,000 at 12% simple interest. At what rate must he invest $200,000 for him to earn 10% overall?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 804476: A businessman has invested $100,000 at 8% and $150,000 at 12% simple interest. At what rate must he invest $200,000 for him to earn 10% overall?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
10% overall is +.1%2A%28+100000+%2B+150000+%2B+200000+%29+
+.1%2A%28+450000+%29+=+45000+
-------------------------
+.08%2A100000+=+8000+
and
+.12%2A150000+=+18000+
-------------------------
Let +r+ = the simple interest rate at
which $200,000 is invested
+r%2A200000+ = the interest earned
----------------------------
+8000+%2B+18000+%2B+r%2A200000+=+45000+
+r%2A200000+=+45000+-+26000+
+r%2A200000+=+19000+
+r+=+.095+
The $200,000 must be invested at 9.5% in
order to earn 10% overall
-----------------
check:
+.095%2A200000+=+19000+
+8000+%2B+18000+%2B+19000+=+45000+
OK