SOLUTION: I invested $2000 more in stocks paying 11% than in an account payomg 6%. If my average interest rate was 9 1/2%, how much did I invest in all?

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Question 304947: I invested $2000 more in stocks paying 11% than in an account payomg 6%. If my average interest rate was 9 1/2%, how much did I invest in all?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The average interest rate is:
(interest income from 11% account + interest income from 6% account)/(total amount invested in both) = 9.5%
Let x = amount invested @ 6%
Then x+%2B+2000 = amount invested @ 11%
%28.11%2A%28x+%2B+2000%29+%2B+.06x%29%2F%28x+%2B+2000+%2B+x%29+=+.095
.11x+%2B+220+%2B+.06x+=+.095%2A%282x+%2B+2000%29
.17x+%2B+220+=+.19x+%2B+190
.02x+=+220+-+190
.02x+=+30
x+=+1500
x+%2B+2000+=+3500
and
1500+%2B+3500+=+5000
You invested $5000 in all
check:
%28.11%2A%28x+%2B+2000%29+%2B+.06x%29%2F%28x+%2B+2000+%2B+x%29+=+.095
%28.11%2A%281500+%2B+2000%29+%2B+.06%2A1500%29%2F5000+=+.095
%28.11%2A3500+%2B+.06%2A1500%29%2F5000+=+.095
%28385+%2B+90%29%2F5000+=+.095
475%2F5000+=+.095
475+=+475
OK