How to Solve Investment Word Problems Involving Interest Rates and Profits?

[bergausstein]

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%

$0.06(8000)+0.085n=0.08(8000+n)$

$480+0.085n=640+0.08n$

$0.085n-0.08n=640-480$

$n=32,000$

\$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 ven-tures. 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!

 

[MarkFL]

1.) Correct.

2.) Let $x$ represent the first investment amount and $y$ represent the other. So we know:

$$x+y=12000$$

And we also know:

$$0.08x-0.04y=120$$

which I would rewrite as:

$$2x-y=3000$$

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 $y$.