SOLUTION: A man has $20,000 invested at 7% and %50,000 invested at 4% simple interest. What additional sum must he invest at 6% to give him an overall return of 5%?

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Question 128549: A man has $20,000 invested at 7% and %50,000 invested at 4% simple interest. What additional sum must he invest at 6% to give him an overall return of 5%?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
overall percent gain = (sum of separate gains) / (total amount invested)
%28.07%2A20000+%2B+.04%2A50000++%2B+.06%2Ax%29+%2F+%2820000+%2B+50000+%2B+x%29+=+.05
%281400+%2B+2000+%2B+.06%2Ax%29+%2F+%2870000+%2B+x%29+=+.05
multiply both sides by 70000+%2B+x
3400+%2B+.06x+=+.05%2870000+%2B+x%29
3400+%2B+.06x+=+3500+%2B+.05x
.01x+=+100
x+=+100%2F.01
x+=+10000
He must invest $10,000 at 6% to have an overall return of 5%