Question

Katie invested a total of $4000. Part at 4% simple interest and part at 5% simple interest. At the end of 1 year the investments had earned $175 interest. How much was invested at each rate?

Answer 1

Answer:  $2500 at 4%   and   $1500 at 5%

Step-by-step explanation:

$\begin {array}{l|c|c|l}&\underline{Amount}&\underline{\%}&\underline{Amount \times \%=Interest\ earned}\\ 4\%\ Interest&x&0.04&0.04x\\\underline{5\%\ Interest}&\underline{4000-x}&\underline{0.05}&\underline{0.05(4000-x)}\\ \quad Total&4000&\times \times &0.04x+0.05(4000-x)\\\end{array} \\\\\\\underline{\text{Interest earned is given as \ 175}}\\0.04x+0.05(4000-x)=175\\0.04x+200-0.05x=175\\200-0.01x=175\\-0.01x=-25\\x=2500\\\\\text{5\% Interest:}\ 4000-x \rightarrow 4000-2500=1500$