Question

5000 is invested at 3 percent interest. how much money must be invested at 5 percent interest so that the total interest from the two investments is 275 after one year

Answer 1

Here's the appropriate equation:

5000(0.03)(1) + x(0.05)(1) = 275

Then 150 + .05x = 275, or

0.05x = 125, or x = 2500

Invest $2500 at 5% for one year.

Answer 2

whatever% of anything is just (whatever/100) * anything.

so, 5000 at 3% will just be (3/100) * 5000, or 150 bucks.

now, if the two investments were to yield 275, we know the first yields 150, so the second investment must yield the difference, or 275 - 150, or 125.

so, what's the Principal to be invested for 1 year at 5% to get 125 bucks in interest from it?


`\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$125\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to (5)/(100)\to &0.05\\ t=years\to &1 \end{cases} \\\\\\ 125=P(0.05)(1)\implies \cfrac{125}{(0.05)(1)}=P\implies 2500=P`