Question

An actor invested some money at 5% simple interest, & $41,000 more than four times the amount at 9%. The total amount interest earned from the investment was $35,260. How much did he invest at each amount?

Answer 1

An actor invested $77,000 at 5% and invested $349,000 at 9%

Explanation:

Let

x ----> the amount invested at 5%

(4x+41,000) ----> the amount invested at 9%

we know that

The interest earned by the amount invested at 5% plus the interest earned by the amount earned at 9% must be equal to $35,260

so

The linear equation that represent this situation is

`0.05x+0.09(4x+41,000)=35,260`

solve for x

`0.05x+0.36x+3,690=35,260`

`0.41x=35,260-3,690\\0.41x=31,570\\x=\$77,000`

`(4x+41,000)=4(77,000)+41,000=\$349,000`

therefore

An actor invested $77,000 at 5% and invested $349,000 at 9%