Question

Alice Gleason invested a portion of $32000 at 9% interest and the balance at 11% interest. How much did she invest each rate if her total income from both investments was $3200.

Answer 1

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.

`\text { simple interest }=\frac{\text { pnr }}{100}`

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,

`\begin{array}{l}{(y * 9 * 1)/(100)+((32000-y) * 11  * 1)/(100)=3200} \\\\ {(9y + 32000 * 11-11 y)/(100)=3200} \\\\ {320 * 11-(2 y)/(100)=3200} \\\\ {(y)/(50)=3520-3200} \\\\ {y=50 * 320=16000}\end{array}`

She invested $ 16000 at 9 % interest and $ 16000 at 11 % interest