
#1
December 6th, 2013,
01:40
1. A trust fund has invested \$8000 at 6% annual interest.
How much additional money should be invested at
8.5% to obtain a return of 8% on the total amount
invested?
my solution,
let
$n=$amount invested @ 8.5%
$0.06(8000)+0.085n=0.08(8000+n)$
$480+0.085n=640+0.08n$
$0.085n0.08n=640480$
$n=32,000$
\$32,000 is the addtional money should be invested at 8.5%. is this correct?
2. A businessman invested a total of \$12,000 in two ventures. In one he made a profit of 8% and in the other he
lost 4%. If his net profit for the year was $120, how
much did he invest in each venture?
in this problem i don't know how will i represent the amount invested in the other venture. please help. thanks!

December 6th, 2013 01:40
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#2
December 6th, 2013,
01:52
1.) Correct.
2.) Let $x$ represent the first investment amount and $y$ represent the other. So we know:
$ \displaystyle x+y=12000$
And we also know:
$ \displaystyle 0.08x0.04y=120$
which I would rewrite as:
$ \displaystyle 2xy=3000$
Now, add the two equations to eliminate $y$, then solve for $x$, then use this value of $x$ in either of the two equations to determine $y$.