# investment word problems

#### bergausstein

##### Active member
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%$0.06(8000)+0.085n=0.08(8000+n)480+0.085n=640+0.08n0.085n-0.08n=640-480n=32,000$\$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

Staff member
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:

$$\displaystyle 0.08x-0.04y=120$$

which I would rewrite as:

$$\displaystyle 2x-y=3000$$

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 $y$.