Respuesta :
Alice Gleason invested $ 16000 at 9 % interest and $ 16000 at 11 % interest
Solution:
Given, Alice Gleason invested a portion of $32000 at 9% interest and the balance at 11% interest.
We have to find how much did she invest each rate if her total income from both investments was $3200.
Let the 1st part of amount be y, then second part will be $32000 – y.
[tex]\text { simple interest }=\frac{\text { pnr }}{100}[/tex]
Where "p" is principal amount
"n" is number of years
"r" is rate of interest
Now, according to given information,
Simple interest for 1st part + simple interest for 2nd part = 3200
Considering to be for 1 year,
[tex]\begin{array}{l}{\frac{y \times 9 \times 1}{100}+\frac{(32000-y) \times 11 \times 1}{100}=3200} \\\\ {\frac{9y + 32000 \times 11-11 y}{100}=3200} \\\\ {320 \times 11-\frac{2 y}{100}=3200} \\\\ {\frac{y}{50}=3520-3200} \\\\ {y=50 \times 320=16000}\end{array}[/tex]
She invested $ 16000 at 9 % interest and $ 16000 at 11 % interest
